Alexei could well join the legion of Alex names popular in the US. There are countless opportunities to exoticize Alexander, and Alexei is one of the most straightforward. Other variations are: ALEXANDROS, ALEXIOS, and ALEKSEI.
Alexei Alexeyevich Abrikosov, Soviet and Russian theoretical physicist and Nobel prize winner
Alexei Romanov (1904-1918), Crown Prince and the only son to the last czar of Russia AlexeiRamirez, Cuban Major League Baseball second baseman and shortstop for the Chicago White Sox
Alexei Vronsky and Alexei Karenin, male lover and husband for Anna Karenina
Alexei Markovic, character in Her Interactive's "Alibi in Ashes"
Alexei 'Alyosha' Karamazov is the main character in Fyodor Dostoyevsky's "Brother's Karamazov"