I just looked into database of Swedish names it is bit out of proportion, it was matter of time when something like this would happen. Write BBs or/and your local LAs (the latter can't do anthing with names already existing) that's all you can do really.
Maybe suggest they should program some feature that would check names on your roster everytime a new player is added and if there is already player with the same name add ", Jr." to the name of the new one.) don't know what to do with triplets and more cause solution like John Smith I, II, III is not natural for every country, maybe adding an abbreviation of a middle name after "junior" is taken (or instead) could work, in alphabet order like
John Smith
John A. Smith
John B. Smith
insert Peter Ericsson in this case.)