IIRC at some point it was revealed that the Senju was actually a clan that was a gathering of many clans (hence why it is named so). The reason they renamed themselves as a Senju was in order to fight as one, under the same bander, but after creation of Konoha, there was no longer need for that, since now they would all fight under the Konoha name and thus could have simply returned to their own original names. Some died. Some mixed. Thus we reach the current stage of the clan, which is so far only one person remaining (under the surname known as Senju, though the Senju's lineage probably survived).
Basically the Senju name lost it's meaning after creation of Konoha and thus after it, was likely only used in order to recognize those that are directly related by blood to Hashirama (brother, children, grandchildren).
Of course taking into consideration Hashirama's declaration, at the time of Madara's "death", if they had been viewed as "dangerous" and "harmful", then they might have been annihilated by Hashirama himself.