perhaps there are no such official titles/functions in a Polish wedding - I am not sure but never heard about such - there are groom's best men and bridesmades and that's all I am familiar with
The term "Ring bearer" is quite problematic. You will find everything you need in this thread: /free-translation-42/wedding-translations-please-best-man-father-groom-52067
The usual word for "wedding ring" in Polish is "obrączka", not "pierścień". So "nosiciel obrączki" would be a literal translation of "ring bearer", and would be more easily understood than any term with "pierścień".
Ussually the polish name for ring bearer is świadek or drużba - as it is a best man who carries rings. (see "Four Weddings and a Funeral "for how good it can end)