Hungarian names

I want to ask about the rules of Hungarian names. I noticed that they use -fi for names according to "son of".

Let's say András Fülöp. If his father is János Fülöp, his name can be written as András Jánosfi Fülöp. However what if his father is also Andras Fülöp? Would it be Andras Fülöpfi or András Andrásfi Fülöp? Is it alternatively to use Sr. and Jr.?