Formally, the Minister of National Defense assigns names to Polish ships. This occurs after receiving an official request from the Navy Inspectorate.
Favorites from public votes are WILK, DZIK, ŻBIK and RYŚ (for gap-filler) and ORZEŁ, SĘP, BIELIK, JASTRZĄB, KONDOR for actual boats.
Hope that helps!
All the best from Warszawa,
Andrzej