I don’t believe this is addressed in-universe. But I think the Lupin family may have had some prior connection to wolves.
The Pottermore entry on Lupin says this about Remus’s birth:
Lyall and Hope's first and only child, Remus John, was born after a year of marriage.
We learn what Remus’s middle name is (although we knew that from an earlier interview), but no further detail is given on the significance of his name. Also note that this was his birth name, and not something he changed later (quashing a theory from the comments, and besides, why would he want to draw attention to his werewolf condition?).
His parents were Lyall Lupin and Hope Hewell, and his father’s name is worth considering further. Quoting from Wikipedia:
“Lyall” is found early in Scotland and was derived from the Old Norse given name “Liulfr” meaning Wolf.
That’s three wolf-based names in the family, which seems more than coincidence.
I’d guess that the Lupin family has a history with werewolves, but that the origins of the name are either forgotten or not discussed. It could be that they had a werewolf in the family (possible since werewolf genes aren’t hereditary; see Teddy for an example) or that an ancestor of theirs helped to subdue werewolves. Personally, I’d think the second is more plausible, but it’s just a guess.
If they did have an ancestor who was renowned for werewolf-related activities, then they might be proud to keep the theme running through the family names. Notice that Lupin breaks this trend, and it seems unlikely that Teddy would have reinstated it. Further, it might make them a high-profile target for existing werewolves, if they were a famously anti-werewolf family.