To compile the Y-DNA results of the men bearing the name (or variant) and or their genetic signatures into meaningful family groups.
Current residence is irrelevant because in due course, we shall see how all families migrated at various times to their new country.The higher the test, the better - my personal recommendation for any male is the autosomal test ('Family Finder') and the Y111 STR Test followed by the Big Y SNP testing.  Luckily FTDNA has regular sales throughout the year although we will not know what will be available until the public notices come out.