Oh, wait. Why you'd think that Ash will get three rivals when Ash won't have any rivals after the League ends (unless you consider Colress a rival)
I think that Rosa (or Nate, but not the two at the same time) could appear soon. Speciually when we doesn't anybody to battle Cheren and we're nearly Aspertia City. Hugh can also appear but has less possibilities.
I think that Ash won't have any real rivals after the League. And because I'm almost sure that Bianca will appear... but wshe will have a 0,00% of rivalry