I came across your question by accident. I studied Polish and lived there for two years. I don’t want to get your hopes up, you could be related. It is the polonized form of the former Lithuanian royal house. I remember that in pre-WWII Poland Poles were forbidded by law to change their surnames to those of the top five noble families in Poland. I don’t think Jagiello was one of them (I don’t think they were around much any longer — a lot married into foreign princely houses and their dynasty was succeeded by the old Swedish Vasa dynasty — which is defunct even in Sweden), but I can’t imagine it would be kindly looked upon by their courts to change one’s name to one of their great dynasties. Just a thought.