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 Nobelist
Alexei Nikolaevich Romanov, Tsarevich of Russia, son of Tsar Nicholas II
AlexeiFernandoRamirez, Cuban baseball player
Alexei Anatolievich Navalny, Russian lawyer, politician and activist
Alexei Nikolayevich Kosygin, Russian Soviet politician
AlexeiDavid Sayle, English comedian
Alexei Eremenko (born Aleksei Alekseyevich Yeryomenko), Russian-Finnish footballer
Alexei Konstantinovich Yagudin, Russian figure skater
Alexei Vyacheslavovich "Alex" Kovalev, Russian ice hockey player
Alexei Andreyevich Cherepanov, Russian ice hockey player
Alexei Vronsky and Alexei Karenin, lover and husband for Anna Karenina
Alexei Markovic, character in video game "Alibi in Ashes"
Alexei 'Alyosha' Karamazov, main character in Fyodor Dostoyevsky's "Brothers Karamazov"