English surnames are generally regarded as falling into seven categories.
The name EATLY does not appear in any of the published dictionaries of surnames.
I suggest it may be a Geographical name derived from a proper name such as EATE and LEA (LEA meaning a wood, a clearing in a wood or a meadow, depending on the stage deforestation had reached when the name was adopted).
Like most amateur philology this is probably complete twaddle.
Any suggestions gratefully received.