Something that only famous historical people had a surname like:

• Longshanks
• Hardrada -Pendragon

Okay Those make you a bit identifiable but i love long double word ones like “longshanks” that sound enough like a common surname to pass scrutiny. Or Nightingale, i.e florence nightingale

I would also look at Scottish clan surnames on wikipedia or scotclans.com - lots of common ones there with overlap to English surnames, like Campbell and Cummings, but also rarer ones like McGregor. Possibly other cultures have a similar such list. Maybe don’t go for spanish surnames if you want to avoid persecution from ICE, idk how bad things are in that regard.