Where does “Birkisson” come from?

Birkisson (Icelandic) comes from Icelandic birki, from Proto-Turkic biŕ — we.

Ancestry of “Birkisson”, step by step

Step	Language	Word	Meaning
1	Icelandic	birki	birch, especially the downy birch
2	Proto-Turkic	biŕ	we