I doubt that will happen. If that was the real intent, it wouldn't make a whole lot of sense for a team that obviously also should include people like Captain Marvel, Shang-Chi and Dr. Strange to be started by Kamala recruiting Kate Bishop. Especially when so many of those people already know each other.
I do think there's a high chance the name 'Young Avengers' won't be used, except maybe as a joke/one-liner, since they obviously didn't cast for a bunch of teenagers. But they're almost certainly intended to be a separate team or at most one of multiple sub-teams of the Avengers, not the singular Avengers replacement team. Possibly they'll use the Champions name, or else maybe call them the 'New Avengers' or something else with less comic book pedigree.