Ash has Southern charm plus the arboreal-nature appeal. Plus your little boy will prize Ash as the name of the hero of the Pokemon cartoons. Ash can also be a dashing short form of Asher, Ashton, or any other "Ash" name.

The poetic, soft-spoken Auden has recently started to be considered as a first name option, used for both sexes, appreciated for its pleasing sound as well as its link to the distinguished modern Anglo-American poet W.H. Auden.

Auden

Alchemy

Anubis

Atlantis

Bucky

Capulet

Devereux

Dobby

Long heard as a last name, as in venerable poet Robert, U.K. talk show host David, British actress Sadie and old Jack Frost, Frost has suddenly entered the scene as a possible first, along with other seasonal weather names like Winter and Snow.
 Some forward-thinking parents are beginning to warm to the icy simplicity of Frost, placing it among the most fitting <a href="https://nameberry.com/list/89/winter-baby-names">names for winter babies</a>.

Frost

A name that crosses cultures, Idris was virtually unknown before the emergence of the charismatic Idris Elba, first on The Wire and then depicting Nelson Mandela in the acclaimed film.
In Welsh mythology, Idris Hawr "the Giant" was a legendary seventh-century Welsh giant and magician who gave his name to a well-known mountain, "Idris's Fort".
In Arabic, Idris means"to learn, study" and is the name of a prophet mentioned twice in the Quran. Idris Shah was a prominent Sufi writer.

Idris

Lumos

Brought into the American consciousness as the nickname of ballet great Mikhail Baryshnikov, it more recently took on a unisex air via TV and screen actress Mischa Barton. Could become the next Sasha. 

Misha

The family name of Shakespeare's Romeo has an effete, monocled image. 

Montague

Moony

Narnia

An evocative unisex one-syllable name, Poe is most distinguished by its literary reference. Edgar Allan Poe was an influential American author and poet, credited with inventing the genres of detective and science fiction, which might provide inspiration for parents who are fans. And now its choice as the name of the hero played by Oscar Isaac in the new Star Wars movie is sure to catapult it from literary choice to major favorite.
 The female singer-songwriter professionally known as Poe was born with the more prosaic name Ann.
 The variant spelling Po is identified with Po Bronson, the chronicler of the technological age, and also has the geographical association with the river in northern Italy.

Roux is the name of the dashing Johnny Depp character in Chocolat. Roux is French from a Latin word meaning russet or brownish red; it's also a cooking term for a mixture of flour and butter that forms the foundation of many gravies or sauces. Most of today's children with this name, pronounced roo, will actually spell it Rue, for the female character in The Hunger Games.

Roux

Rhapsody

Salem is a Biblical place name in Canaan, believed to be the same as Jerusalem, as well as the Massachusetts town famous for its late 17th century witch trials. Salem is also a popular first name in its own right throughout the Arabic world.

In the US, about 400 babies of both genders were named Salem last year, but it's difficult to say how many of those were given the Biblical place-name and how many the Arabic version of the name. About 40 percent of the Salems were boys, with a significant number of baby boys given an alternate spelling of the Arabic name, Salim. 

One negative association of the name, the menthol cigarette, went out of business in 2019

Salem

While Skylar is currently the most popular spelling choice for girls - and the spelling seen most often - the Skyler option is more (statistically) unisex. Given to boy and girls in nearly equal numbers each year, it ranks around the middle of the US Top 1000 and is given to more than 400 boys every year.
 
Derived from the Dutch surname Schuyler meaning "scholar", this spelling emerged in the 80s and was likely inspired by the popularity of the name Tyler.

Skyler

Stevie

Thisbe

Allie_J's list "Names for Future Pets - Unisex Edition" of 24 great name ideas: Ash - Thisbe!

Names for Future Pets - Unisex Edition

These are the names I'd consider for future pets but haven't thought about whether they'd be for female or male. They could work for either I guess, but I'm going to leave it on the 'male' setting as that's the default.