DNA Phillips name

[hdw]

If the story is true, I suspect that the Scottish surname was Philp or Phil(l)ip, which are both not uncommon here.
Robert Burns's family name was actually Burness, but his father Willliam Burness moved from the north-east of Scotland to Ayrshire, where the name Burns was commoner. After William Burness was dead, his sons Robert and Gilbert changed the family name to Burns.
I had ancestors called Familton, and I know of a descendant of the family who has documentary evidence of an ancestor changing the name to the more familiar surname Hamilton.
Harry