Hello Karenlee
Yes there are lots of folk with this surname and variant spellings, Eburn/e, Eborn/e etc.
My group are Eburne's in Coventry. family with as I said many spellings, go back to the dim and distant past in that city, not that I can get back that far.
You could try there. Allesley and Ryton on Dunsmore are other places you could try. All Warwickshire.
Sorry, my family does not include yours as far as I know.
There was a massive data base on the net - all variants of Hepburn, which included Eburne, but I have lost a lot of info recently and now cannot find it. Does anyone else know about it?
Good Luck
Pelican