Aside from Hashirama, the Senju don't seem to have any unique Kekkei Genkai, so it would make sense for them to intermarry into other families in Konoha (and elsewhere). On the other hand, clans like the Uchiha and Hyūga tended to marry within their own clans, as to better preserve their bloodlines.
So, I'm guessing between wars and intermarriage the Senju name eventually died out. But Kishimoto could always take the darker path and later reveal that the Senju were exterminated, much like their Uzumaki cousins. We'll have to wait and see.