I'm reading the fascinating The Romanovs by Simon Sebag Montefiore at the moment, and I have been struck by the number of Scottish names that crop up. There was Countess Praskovya Bruce, a confidante of Catherine the Great, whose husband, James Bruce was governor of St Petersburg. Fife-born Samuel Greig was a distinguished admiral of the Russian fleet, Patrick Gordon was a general who fought for Peter the Great, and the Cameron Gallery in the royal residence Tsarskoye Tselo is named after Scottish architect Charles Cameron. The name Mary Hamilton crops up several times in different generations, the most famous Mary Hamilton being a lady-in-waiting of Catherine I, Peter the Great's wife. She was executed in 1719.
I came across a very interesting article on Russian place names that have a Scottish origin (pdf version here), which looks at the history of Hamiltons in Russia and notes that the name Hamilton was russified and became, first, Khamaltov, and then Khomutov. There are various villages in southern Russia and Ukraine, and street names in other places, that are all variations of Khomutov.