Once a popular choice in for boys in the Middle Ages and again during the 19th century, Aubrey has mostly been used for girls in the US since the 1970's. With its arty, surname-y, and sophisticated feel, however, it is rising up the UK charts for both boys and girls. 
Derived from the Auberi, an Old French variant of Alberich, Aubrey means "elf ruler". Up until the 50's, it was relatively well known for boys in the US, but with the release of the song "Aubrey" by Bread in 1972, the scales tipped. 
Despite this, there are still memorable male bearers of the name, including rapper Drake, whose full name is Aubrey Drake Graham; the 19th century illustrator Aubrey Beardsley; and the central character of John Polidori's novel The Vampyre. 
Used on only a tiny handful of boys each year in the US, in the UK, Aubrey is currently in the Top 250 for girls, but also the Top 600 for boys. This means it is given to boys 5 times more often in the UK, than it is the US. 
Gentle, cool and handsome, Aubrey fits in with the recent interest in softer boys names and in surnames-as-given-names. Plus, with Ellis, Mckenzie, Hadley, Casey, and Oakley in use, Aubrey might see further gains.

Aubrey

Adeline

Alba

Aria 

This word name entered the US Top 1000 for both genders in 2015, though it premiered a little higher for girls. There are still more baby girls named Briar than baby boys -- 594 vs. 361 in 2021 -- but it's rising in popularity for both.

Briar fits the trend for <a href="https://nameberry.com/list/329/nature-baby-names">nature names</a>, and it also offers a fresh option for honoring a Brian.

Briar

Betsy 

Cora

Cordelia 

Delilah 

This Biblical name was rising dramatically for boys, but has plateaued in recent years. Although it's more popular for girls, it's a delightful unisex choice. Eden is one of the <a href="https://nameberry.com/popular-names/france">Top 100 Boy Names in France</a>.

Eden

Evokes 1960s brotherly close harmony. The Red Hot Chili Peppers' Anthony Kiedis named his son Everly Bear, and it is also an explosively popular choice for girls. We predict that all the "Ever" names will be one of the defining trends of the 2010s-20s.

Everly

Eleanor 

Elizabeth 

Elodie

Elsie 

Eva 

Florence

Harper got its start as a celebrity baby name when Paul Simon chose it for his now-grown son. Since then, other famous parents have followed suit: musician Tim Finn and actor Cecilia Peck both have sons called Harper.

Other high-profile Harpers, like author (Nelle) Harper Lee and starbabies Harper Burtka-Harris and Harper Beckham, are female, but it makes a handsome choice for either sex (and is in the US Top 1000 for both boys and girls).

Harper

Hillary

Harriet 

Isabella 

Isla 

Luna

Mirabella

Piper's rising popularity for girls makes it an unlikely masculine choice.

Piper

Penelope 

Poppy

Most of the notable Rivers have been male, but this nature name certainly flows as well for a girl. The name River is still rising for both genders, with about 3500 baby boys receiving the name last year vs. 1900 baby girls.

Kelly Clarkson's choice of River for her newborn daughter further raised the profile of the <a href="https://nameberry.com/girls-names">name for girls</a>. Baseball great Derek Jeter and Hannah Davis used the same name as Clarkson for their daughter born in 2021, River Rose.

River

Rosalie 

Willow

S0phiewils0n's list "Baby girls names for my child" of 30 great name ideas: Aubrey - Willow!

Baby girls names for my child

Baby names for girls that I'm considering - love names that sound different but aren't too out there, something that's easy to grow into.