Not commonly; but sometimes for a variety of reasons Jews do have names that are not commonly Jewish. These reasons may include name-changes, adoptions, a non-Jewish father marrying a Jewess, etc. Also, on arrival at Ellis Island, European Jewish immigrants to the U.S. in 1880-1920 often took American names.
Mick Thomson from Slipknot's full name is Mickael Gordon Thomson
Cassi Thomson's birth name is Cassi Nicole Thomson.
Cyndi Thomson's birth name is Cynthia Evelyn Thomson.
Frederick Thomson's birth name is Frederick Clifton Thomson.
Kenneth Thomson's birth name is Thomson, Charles Kenneth.
Mick Thomson's birth name is Mickael Gordon Thomson.
Pat Thomson's birth name is Patricia Elizabeth Thomson.
Penny Thomson's birth name is Penelope Louise Thomson.
Virgil Thomson's birth name is Thomson, Virgil Garnett.
Gabriel Thomson's birth name is Gabriel Francis M. Thomson.
Lionel Thomson's birth name is Peter Lionel C. Thomson.
Lord Thomson of Fleet's birth name is Thomson, Roy Herbert.