Unfortunately, short of living in Russian, this will be a hard name to swallow. Why? Not necessarily itself being the problem... simply that (especially in the United States) "Aleksey" will be viewed as a "kre8tiv" variant-- an uneducated decision. Regardless of that fact, if you possess a true Russian surname I believe that this could be pleasant. "Aleksey Anderson"? I an afraid not. "Aleksey Dobrokhatova"? Very desirable. May I add: This should be strictly a male title. I apologize, women... but that opinion should be obvious of reason.
I like this name. It's different and very rarly used in the USA for boys. I only know two guys with this name. Hope to name my 1st born son Aleksey Robert (after the last Tsarevich and after my grandpa).