How did the Hyuga clan come to be?
Before going to the moon, Hamura's bloodline on Earth continued, which eventually would become the Hyūga clan and the Byakugan was also passed down to them.

There is no mention of Hamura's love life or his children, but at this point the only logical explanation would be that his lineage continued through someone (who's never shown in the anime) and thus formed the Hyuga.

Also, there is a direct descendant of Hamura Otsutsuki mentioned in "Naruto: The Last" movie belonging to the same clan, Toneri Otsutsuki not exactly someone who is responsible for creating the Hyuga clan.

Here's more about Hamura Otsutsuki, his lineage and abilities: Hamura Tsutsuki wiki