Here's the information we found on the name "Geillis."
This is a medieval Scottish name which was used by both men and women. We found the spellings "Gelleys" and "Gelis" (both women) from the 16th century. (1)
We found related names in Flemish and French. Flemish has the following forms (2):
French (which was spoken in Flanders and Brittany) has (3):
Metronymics were rare, but used, in Welsh and Flemish. We haven't found any examples in Scotland. We have little information about Breton names, but since they were heavily influenced by French, which did use metronymics, we would guess that they were used.
Talan Gwynek, Effric neyn Kenyeoch vc Ralte, Walraven van Nijmegen, Tangwystl verch Morgant Glasvryn, and Arval D'Espas Nord contributed to this letter.
We hope this has been helpful, and that we can continue to work with you.
Academy of S. Gabriel
(2) Debrabandere, F. "Kortrijkse Naamkunde 1200-1300, met een kumulatief familienamenregister"
(3) Catledge, S. "Names from the Paris Census of 1292." In the "Proceedings of the 1996 Known World Heraldic Symposium."