Bartholomew is an apostle's name that's been out of favor for centuries but might appeal again to the parent in search of an old but rare choice. The challenge could be to avoid the Simpson-ish nickname. That character, by the way, has the full name of Bartholomew JoJo Simpson, and creator Matt Groening came up with Bart as an--uh oh--anagram for brat. Two old alternate nicknames are Barty and Tolly.
 Ben Jonson's 1614 comedy Bartholomew Fair is set in London on St. Bartholomew's Day. Charles Dickens used the name in Bleak House, and, more recently, Bartholomew Cubbins is the protagonist of the Dr. Seuss books The 500 Hats of Bartholomew Cubbins and Bartholomew and the Oobleck

Bartholomew

An x makes any name cooler, so that Baxter has a bit more pizzazz than the original Baker. Baxter had some currency as a first name a century ago--it was on the popularity lists sporadically from 1880 till the 1920s, peaking at Number 515 in 1886-- which means it's just about due for a comeback. And we can see Bax as a worthy follow-up to Max and Jax.
 Singer Ian Dury named his now-grown son Baxter, and Dr. Baxter Stockman was a scientist in the "Teenage Mutant Ninja Turtle" series. 
 Fun feminist fact: as an occupational name, Baxter was actually the word for a female baker. It's only used for boys now, but could legitimatelt be a unisex name.

Baxter

An old English redhead name -- one of the few that doesn't begin with the letter r -- with references both to a famous French knight and a magical horse. 

Bayard

Beckett is one of the big baby name hits of the decade.
 A handsome name with an attractively brisk sound, and rich in literary associations via major Irish playwright Samuel Beckett, it is especially hot among celebs. Melissa Etheridge jump-started the trend in 1998, followed by Conan O'Brien, Stella McCartney, Malcolm McDowell, Nicole Sullivan and Natalie Maines.
 Another worthy namesake is the martyred saint Thomas a Becket, Archbishop of Canterbury, whose story was the basis of the Anouilh play "Becket," which became a film starring Richard Burton and Peter O'Toole.
 In 2005, the authors of Freakonomics predicted that Beckett would be one of the most <a href="https://nameberry.com/popular-names">popular baby names</a> of 2015. Although they were a little off the mark -- Beckett hasn't even cracked the Top 100 -- we predict that it will continue to climb the US rankings.

Beckett

BEDIVERE

Bellamy is a surname name with an admirable meaning and upbeat rhythm, similar to jovial choices like Rafferty, Barnaby and Willoughby. 

 Bellamy is rising simultaneously for boys and girls at the moment, making it a truly gender-neutral choice. It entered the Top 1000 for girls for the first time in 2018, before dropping out in 2019 and entering for boys. Since 2020, Bellamy has finally been in the Top 1000 for both genders.

 Muse frontman Matt Bellamy and Bellamy Blake from The 100 are notable male namesakes.

Bellamy

BELLANGERE

BELLIS

BELTAIN

This Italian form of Benedict sidesteps the Benedict Arnold association that still clouds the English version. 

Benedetto

Parents who like Ben and Benjamin but find those forms too popular sometimes consider Benedict as a more distinctive choice. Unlike the Old Testament Benjamin, Benedict is the name of the saint who formed the Benedictine Order and of fifteen popes,including a recent one. 
 Shakespeare used a variant form--Benedick--for the character in Much Ado About Nothing. Other options are Bennett and Benno.
Benedict Cumberbatch is a rising British stage, film and TV actor, who has been seen as Stephen Hawking, William Pitt, Dr. Frankenstein, Frankenstein's monster, and currently as Sherlock Holmes in the BBC series.
 Just one caveat: There is the link to that infamous traitor Benedict Arnold.

Benedict

Smoldering Spanish actor Benicio Del Toro made this version an American possibility. It debuted on the US Top 1000 in 2016, when it was the third-fastest-rising boys' name.

Benicio

Benito

Bennett is Ben with a bow tie, kind of a cross between Benjamin and Beckett. It's been trending up on the popularity charts in recent years, and its choice by The Unbreakable Kimmy Schmidt's Jane Krakowski could shoot it even higher. 
 Bennett Cerf was an eminent publisher--one of the founders of Random House--and renowned punster.
 Bennett is a popular surname, and has many noteworthy bearers, from Jane Austen's Pride and Prejudice family (with one 't') to indomitable singer Tony. Bennett has been used as a surname in England since the early thirteenth century.

Bennett

Benno is a cool name in its own right -- there was a tenth century Saint Benno -- though it is also used as a lively nickname for Benjamin. Saint Benno of Meissen is the patron saint of anglers and weavers and, strangely enough, alliteration.
 Benno came to attention in the U.S. via the father and son duo of Benno Schmidt Sr. and Jr. Senior was the venture capitalist who invented the term venture capitalist and Junior was the president of Yale University. Benno is also the appellation of a student character in Umberto Eco's The Name of the Rose.

Benno

Benton is an old English surname of a type usually given to local landowners. It is also recorded in early records as Beneton and Bentune. Benton newly returned to the Social Security list in 2011 after a forty-plus year absence, perhaps as a fresh route to Ben.

Benton

BERDIC

Last-name-first-name with a romantic but dangerous edge. 

Berenger

Berwyn

This Irish name of a saint from the Isle of Aran also appears in myth and fantasy fiction, giving it an intriguing, mystical air. 
 Some modern parents are attempting to update the spelling, as in the actor Breckin (middle name Erin) Meyer or the most popular form of the name, Brecken.

Breccan

Surname name with feminine final ley. The Welsh name Bryn, though also unisex and veering toward the girl world, is far more attractive. 

Brinley

The simple and attractive Bryn is well used for boys in Wales, and does have a history as a male name in the US, although both Bryn and Brynn are currently far more popular for girls.

 Fans of British TV sitcom Gavin and Stacey will recognize it as the name of Stacey's lovable and eccentric uncle, played by Rob Brydon.

Bryn

octobertales's list "B - Boys' Names" of 22 great name ideas: Bartholomew - Bryn!