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yes, it should. But sometimes little Russian kids say "хочете" too. :lol:

I think you should transliterate what's written in your passport.

His parents would choose the modern variant, of course, which will be written in his birth certificate and I doubt that he would prefer being called Матфей.

Actually, Матфей and Матвей are two variants of the same name, only the latter is a modern one and the former was used in the past and is also an ecclesiastical name.