Ewan McVicar: Quite a few sources, summarized in the review article "Maid-of-Honour Hamilton" by M. I. Semefsky, in _Slovo i Dyelo_ (Word and Deed), St Petersburg, 1885. Child summarizes the article at some length: "When the Hamiltons first came to Russia does not appear. Artemon Sergheievitch Matveief, a distinguished personage,... married a Hamilton, of a Scottish family settled at Moscow, after which the Hamilton family ranked with the aristocracy."

I suppose the name would have become "Gamil'ton" in Russian.