Adam -- a primal Old Testament name -- was revived as a 1960s cowboy name. Adam is not as popular as it once was and feels ready for a respite, replaced by newer A names like Aidan/Aiden, Avery and Axel. Its most prominent current bearers include Adams Sandler, Levine, Brody and Driver -- who plays a character named Adam on Girls.
 Adam, of course, is the first man God created. It is also a generic term for mankind. Adam did not hit the U.S. Top 100 until 1970, peaking in the early '80s at Number 18.

Adam

Anastasiya

Cultured and cultivated in an old-style, Old World way. Sometimes associated with the classic writer Anton Chekhov. Al Pacino has a son with this name.

Anton

Andriy

Dariya

Demyan

Daryna

This simplified version is not nearly as popular as the original (it also destroys a perfectly good palindrome), and has been on the decline in recent years. 

Hanna

Halyna

Iryna

Kalyna

Kateryna

Lesya

Liliya

Larysa

Russian, Ukrainian, and Bulgarian form of the classic Maria sure to cause a lifetime of spelling questions and pronunciation mistakes.

Mariya

Marko

Nataliya

This chic Ukrainian form of Helen is relatively unknown outside of its native country, but it definitely has international appeal. Olia or Olenka are the usual Ukrainian diminutives, but tomboyish Oli or Leni could work too.

Olena

Roman is an ancient name trending in a major way. A surprise hit name of recent years, Roman now ranks in the Top 100 not only in the US but throughout the English-speaking world, and is rising in other European countries as well.
 
Roman owes much of its current popularity to celebrity and pop culture references. It's the name of the youngest son, played by Kieran Culkin, in the TV show Succession. Roman was used for their sons by Cate Blanchett, Debra Messing, and Molly Ringwald.
 Well known Romans include disgraced director Polanski (born Raimund), Polish photographer Vishniac, and onetime star quarterback Gabriel. Francis Ford Coppola has a son named Roman, who is a director now himself.
 Several relatives of Roman are also newly stylish, from Romy to Romilly to Romeo. Definitely a romantic name, however you use it. 
 The French version is Romaine -- and literary parents might appreciate the fact that 'roman' is the French word for novel.

Roman

Sofiya

Symon

Adding a final a to Tamar lends it a more sensual Slavic tone, making it a more popular choice than the original. 

Tamara

The Viktor form of this classic name is widely used throughout Europe and is rising in the US as well.

Viktor

Vira

Valentyna

Viktoriya

Common Russian name familiarized here via cosmonaut Yury Gagarin and a character in Dr. Zhivago, but we don't see it ever gaining permanent resident status.

Yuri

Now that Zoe is getting wildly popular in the U.S. and the U.K. -- one poll puts it at number one in Wales -- parents may start hunting down fresh twists like this. 

Zoya

frauleinawesome's list "Awesome Ukrainian Names" of 29 great name ideas: Adam - Zoya!