Aleksandra is the preferred spelling in many Eastern European languages and cultures, but for English-speakers it's ironically more confusing if also perfectly phonetically clear.

Aleksandra

Aleksei

Anatoli

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

Anya is a Russian variation of Anna, which came from the Hebrew name Hannah. Anya is the form found most frequently in Russia, Poland, and other East European countries, while Anja is the spelling usually preferred in Germany Norway, Denmark, Germany, Sweden, and The Netherlands. In the Hungarian language, Anya also means mother.
 
It is often used as a character name with a bit of foreign flair. Aside from its authentic use in Chekhov's The Cherry Orchard, Anya has appeared as Audrey Hepburn's name in Roman Holiday, on Buffy the Vampire Slayer, and as the latest Spider-Girl, who is also known as Arana. In literature, Anya Seton is the pen name of Ann Seton, author of such best-selling mid-century historical novels as Dragonwyck.

Anya

Arkady is a rhythmic Russian saint's name from the Greek meaning "from Arcadia." As a literary name, it belongs to a genteel character in Turgenev's Fathers and Sons and a much less benign one in Dostoyevsky's Crime and Punishment, and is also a key figure in Gorky Park by Martin Cruz Smith.

Arkady

This international variation was publicized by Olympic skater Ekaterina Gordeeva.

Ekaterina

Evgenia

This variation of Theodore is familiar here mostly via the great Russian novelist Dostoyevsky. It was also the name of three early tsars of Russia.

Fyodor

Commonly used in Russia, has an Old World Slavic feel.   The original Galen can be used for girls as well as boys.

Galina

Gavril

Irina is a Russian ballet-inflected classic, one of the Three Sisters in the Chekhov play.  While some Americans will pronounce this like Irene with three syllables, the pronunciation used throughout Europe, where it's widely used, starts with a short i as in it or if and a strong emphasis on the second syllable.

Irina

Isidore and variants are remarkably underused and ripe for revival, a la Theodore and company.

Isidor

Though some might find it a bit heavy-booted, Ivan is one of the few Russian boys' names to become fully accepted into the American naming pool.
Ivan is, of course, ubiquitous in Russian culture. There is one of the brothers in The Brothers Karamazov, the protagonists of Tolstoy's The Death of Ivan Ilyich, and Solzhenitsyn's One Day in the Life of Ivan Denisovich, and the title character in Chekhov's Uncle Vanya. Real life Ivans include writer Turgnenev, biologist Pavlov, tennis player Lendl, and rulers Ivan the Great and --oops--Ivan the Terrible. Vanya is his warm and appealing nickname.

Ivan

A rarely used Slavic name until the Czech-born ex-Mrs. Trump took it over the top. Daughter's name Ivanka adds a dollop of charm. 

Ivana

This sweet and loving name, favored in recent years by a mix of Hispanic-American parents and Bob Dylan fans, was chosen for her daughter by TV actress Melina Kanakaredes. 

Karina

Kiril

Ksenia

One of the most familiar Russian names in the West, thanks to ballet great Mikhail Baryshnikov and state head Mikhail Gorbachev.

Mikhail

Nadezhda is more familiar in the English-speaking world by its short forms, Nadia or Nadya. Well-used through the Slavic countries and Russia, Nadezhda was the name of Lenin's wife. Viewers of The Americans</a> learned that this was the original Russian name of the spy known as Elizabeth Jennings, played by Keri Russell.

Nadezhda

Perfect <a href="https://nameberry.com/list/412/christmas-baby-names">name for a little girl born at Christmas</a>. Its many variations and pet forms include Natalia, Nataliya, Natalie, Nataly, Natascha, Talya, Talia, Tasha and Tasya.

Natalya

Russian forms, like Russian supermodels, are hot these days. This is a strong, worldly way to make Nicholas new; it was chosen for his son by Barry Bonds, Jr.

Nikolai also comes with several attractive nickname options, including approachable Nik, spunky Niko, or even hip Kai. A traditional nickname for Nikolai in Russia is Kolya. 

Nikolai

For Americans, may prove too much of a twist on Peter. 

Pyotr

Known in America via the wife of Soviet head Mikhail Gorbachev; a possibility for parents of Eastern-European descent wanting to move beyond Natasha and Nadia or for parents from the Middle East looking for a name that works in both cultures.

Raisa

Well used in Russia, this is a distinctive and undiscovered choice here. 
Rodion Romanovich Raskolnikov is the fictional protagonist of Crime and Punishment by Feodor Dostoyevsky.

Rodion

Romantic name used throughout Europe, though sure to lead to pronunciation problems here. Though it's never been too widely used in the US, it's quite popular in Switzerland, France, Austria, and Romania.

Valentin

Vasiliy

Vera was the height of fashion in 1910, then was for a long time difficult to picture embroidered on a baby blanket. Now, though, it has come back into style along with other old-fashioned simple names such as Ada and Iris. 
 Vera was barely known in the English-speaking world until it appeared in the 1860 novel by Ouida, Moths, and Vera Rostov is a character in War and Peace, published nine years later.
 Vern Yip has a young daughter called Vera, and Vera Wang and Vera Famiga have modernized it. Vera Lynn was an iconic British World War II singer, Vera Miles was a Hitchcock star best known for her role as Lila Crane in Psycho and Vera-Ellen (born without the hyphen) was a dancing partner of Fred Astaire and Gene Kelly.

Vera

Vladimir is a cultured and deep-rooted Slavic name associated in this country with cultural figures including piano virtuoso Vladimir Horowitz and the author of Lolita, Vladimir Nabokov.

 The name Vladimir is rich in history, notably borne by Vladimir the Great, the 10th-11th century ruler of Kievan Rus' who brought Christianity to his nation and is now venerated as a saint in the Eastern Orthodox Church. Among the name's other famous – or infamous – bearers are several Russian political figures past and present, including Bolshevik leader Vladimir Lenin and current Russian president Putin. 

 Volodymyr is the Ukrainian form of the name, recently made internationally famous by Ukraine's president Volodymyr Zelenskyy following the Russian invasion of his country. Other variations of this name in other European countries include Valdemar and Waldemar. All derive from Slavic roots vladěti, meaning "to rule," plus meru "great" or miru, "peace" or "world." Common Slavic diminutive forms include Volodya, Vova, Vladan and Vlatko.

 Long a common name throughout the Slavic world, Vladimir is featured in novels by Turgenev and Pushkin. Vladimir also has vampirish connections: Dracula is based on Vlad III, three-time ruler of Wallachia in the 15th century, otherwise known as Vlad the Impaler. A more modern literary character is Vladimir, one of the two main figures in Samuel Beckett's play Waiting for Godot.

Vladimir

Vitaliy

One of many international versions of this classic. 

Yelena

miraje's list "Favorite Russian Names" of 31 great name ideas: Aleksandra - Yelena!

Favorite Russian Names

Great names that I would often have issues using in the US because they really sound at their best with Russian pronunciation.

Boy's and girl's are listed roughly in order of my preference.