If you change a forum name, one simply redirects to the other automatically, so it wouldnt affect it. In fact the name in the URL is simply for the human readable aspect. It's the number that makes the diferrence.
For example, the URL for this forum is
https://invisioncommunity.com/forums/forum/497-help-support/
But if you go here, it goes to the same place, as the ID is the same
https://invisioncommunity.com/forums/forum/497-its-almost-christmas/