As Bas, it's a popular name in The Netherlands, but Baz, as in director Luhrmann, has potential for independent life too.
Curiously, Australian-born Moulin Rouge director Luhrmann was born neither Sebastian nor Basil, but had the name Mark Anthony on his birth certificate; his nickname arose from his supposed resemblance to a British TV fox puppet named Basil Brush.

Ben, the diminutive of Benjamin or Benedict, can easily stand on its own as a simple, strong, nice-guy choice, though it's somewhat attenuated. Ben is this generation's Bob or Bill. 

Bix is a cool and jazzy nickname name, thanks to that final x. It's largely associated with the legendary and influential cornet player (and inspiration for the novel Young Man With a Horn), Bix Beiderbecke. He was born Leon Bismark Beiderbecke and his nickname derived from his middle name.
 Bix could easily fit in with cousins Jax, Dax, etc.

Cal is a nickname style name that feels as friendly and calm as it does cool and breezy. While its longer forms have proved more popular over the years, Cal as a stand alone has dropped on and off of the US Top 1000 since the 1880s.
 
Traditionally, Cal derives from the Biblical Caleb, giving it the meaning "dog" or "the whole of". Alternatively, it comes from the English name Calvin, meaning bald. There are however a multitude of other origins, including Callum, Callahan, Callan, Pascal, Connally, Calix, and Macauley.
 
You could go for one of these long forms if your prefer something more formal or with a more solid meaning, but Cal as a standalone name has a long history of use. Since US records began, there has never been a year when it wasn't given to at least 5 babies, and. as of 2020, it is back in the US Top 1000 and on the rise.
 
Given to around 370 babies each year, Cal fits in with other nickname style names, like Leo, Jack, Finn, Ty, Drew, and Mack.

Cameron is still more popular as a boy's name than a girls and this simple, snappy short form works well for either sex.

May be the most modern, stylish Catherine nickname: more unusual than Kate or Cate, with an animal and word name edge.  Cat Power is a trendy folksinger.

During the heyday of Deborah, Debra, and Debra -- the late 1950s and early 60s -- there were enough baby girls named Deb, just Deb, for it to make the Top 1000.

Today, Deb is literally extinct for babies, though there are plenty of grownup women called Deb.

Flo is an antiquated nickname not often used these days, possibly because "Aunt Flo" is a euphemism for a period. 

Gus is a homey grandpa nickname name that can work as a short form for any of the above or stand on its own as a cutting-edge replacement for Max and Jake--though it was off the Top 1000 from 1978 until 2016, when it squeaked in at Number 999.
 Gus was chosen for their sons by Dixie Chick Emily Robison and actress Julie Bowen. In T.S. Eliot's Old Possum's Book of Practical Cats (and in the stage musical), the full name of Gus the Theatre Cat is Asparagus.

There was an eighties cartoon queen named Jem (& The Holograms), and this is as likely to be a full name as a short form – deriving from Jemma, Jemima or Jameela.

This super-charged variation of Jett is on the rise -- along with the unlikely newcomer Jetson.

Peaked in the 1940s, but still an amiable classic, a la Joe and Tom -- though rarely used on its own. 

Streamlined version of the classic boys' names, sometimes a short form of Jonathan, which is in fact an entirely different name from John attached to a different Biblical personage. Jon feels more modern than the traditional John, but some may find it an overly slight variation on an already slim name. Jon Snow is a popular character on HBO's Game of Thrones.

A simple and charismatic Chinese and Korean name, also spelled Joon.

Kai is an internationally flexible name with many possible origins and meanings, growing in popularity in the US and a diverse range of European countries.
 
In the US, the name Kai is most commonly referred to as being of Hawaiian derivation, meaning "sea." In Europe, Kai is largely considered to have Frisian origin as a diminutive of the name Kaimbe, meaning "warrior", or as a short form of Gerard "brave spear". 
 
Kai is also found as an independent name in African, Chinese, Turkish and Native American cultures. Kai is a strong, evocative multi-cultural name that packs a lot of power in its single syllable. 
 
Famous as the name of the boy enchanted by the fairy-tale Snow Queen, Kai was chosen for her son by actress Jennifer Connelly and as a middle name for son Samuel by Naomi Watts and Liev Schreiber. 
 
Kai is popular with Berries as both a first and middle name choice. Perhaps because of its international familiarity, Kai is popular in video games. Its most prominent namesake is Danish-born jazz trombonist Kai Winding.
 
Kai ranks in the US Top 1000 for girls, but is used more than 90 percent of the time for boys. Donald Trump, Jr. has a daughter named Kai Madison and Gigi Hadid and Zayn Malik named their daughter Khai in 2020.

As attractive and straightforward as Kir may be, you may wish to go with the Irish spelling Keir (of different origins), due to Kir's association with the French cocktail.

Kit is a crisp, old-time nickname with plenty of spirit and style. In the UK it's a rising star for boys, while in the US, it is trending upwards for girls too. Originally used as a diminutive of Katherine and Christopher, Kit could make a cool alternative to Katie, or an unexpected honor name for the aforementioned classics. 
 
Coinciding with the name for a young fox, Kit feels at home with the likes Wren and Quinn — and with fast risers like Scottie, Robin, and Drew. In 2023, around 130 girls received the name compared to 180 boys. 
The year prior, however, the scales were tilted the other way, with 160 girls and 140 boys receiving the name. With its unisex potential then, and its sharp, clear sounds, Kit may well see more use across the board in coming years. 
 <
Love the idea of Kit for a girl but still want a full name that isn't Katherine or Christina? You could try Kallista, Kensington, Keturah, Kismet, Kinneret, or Katalina.

In Ireland and Scotland, Mac and Mc mean "son of"; here, Mac is a generic fella, or a short form cooler than either Matt or Max. Mac can be a nickname of any longer Mac or Mc starting name such as McCoy or Macalister. If you want to make it feel more complete, you can always spell it Mack.

Though most Mels are playing pinochle with Murray and Morris, there was a notable Saint Mel. He is one of the earliest Irish saints, a nephew of St. Patrick.  He became a  priest, then built a great monastery where he served as abbot.

Bobbsey Twins-era nickname name that could find new life via Nan, heroine of The Nanny Diaries. Nan was also the nickname of Annabel St George, the protagonist of Edith Wharton's novel "The Buccaneers".

Just the kind of old-fashioned nickname coming back into style. 

This mild-mannered short form was Queen of the Prom in the fifties and sixties, but today is mostly heard on TV's The Office (and of course as one of the founders of Nameberry).

While about 100 baby girls are still named Pamela in the US every year, the name Pam is now officially extinct.

Paz, currently represented by actresses Paz Vega and Paz de la Huerts, would make a sparkling middle name choice. It originated as a title of the Virgin Mary, Our Lady of Peace, and is one of the <a href="https://nameberry.com/list/411/baby-names-that-mean-peace">names that mean peace</a>, derived from the Latin word "pax".
 Pazia is an attractive elaboration, while Pazit (pronounced Pah-ZEET) and Pazya are Hebrew variations. Paz in Hebrew means "gold".

The short, cute Pim is a Top 100 boys' name in The Netherlands though little-known outside that country.  But in a family overrun with Williams, Pim could make an original nickname setting a modern child apart from father Will and grandpa Bill.

The original Pip was the main character in Great Expectations (full name Philip Pirrip). Cute for a tike, maybe too cute for an adult.

With the return of the less obvious virtue names such as Verity and Prudence, vintage nickname names like Pru may follow in their wake.

Fiery but slight middle name choice; much more apt to be a redhead's nickname. 

A sweet and simple Japanese name with several possible meanings, depending on the kanji characters used.

A very popular girls' name in Japan whose sound is consistent with its meaning.  Another possibility is Ren.

The Biblical Simon has been rediscovered and this appealing short form, an alternative to Sam, might be a way to make your Simon even more special.

Although pinochle-playing partner Sam came out of retirement, we don't see it happening to Sol. Near soundalike Saul has more of a shot.
Sol was also a Roman god/personification of the sun, and an epithet of sun-god Apollo.

A unisex Hebrew name often found in combination with others, as in Tal-El and Tal-Or.

Like Ed, Eddie and Teddy, Ted is rarely used as an independent name – in the US, at least. In the UK, Eddie ranks just outside the Top 200, Teddy ranks just outside the Top 30, and Ted is a Top 200 pick. 
With Theodore rising, Ted may have new life among parents who don't want to use the short form Theo. And TV's Ted Lasso makes it a quintessential nice guy name.

Tim is a boyish short form very rarely given on its own. 

Occasionally used as an independent name, but why. 

Minimalist nickname via XXX star Diesel (born Mark Vincent). 

SorklaMenli's list "Lojban Cunrafsi Names" of 48 great name ideas: Baz - Vin!

Lojban Cunrafsi Names

Short and sweet 3-letter names that just happen to be rafsi.
Rafsi are combining forms of words that can be strung together to make compounds, and can be used as nicknames (or as names in their own right) in the Lojban-speaking community.