One place where you can look for "Jewish" names is in the book "When Scotland Was Jewish", which you can get by interlibrary loan.
It was too expensive to buy, over $50, and not available at my library, but they were glad to send for it. It lists a number of names which
the authors think were Jewish in the Middle Ages.
Some people have declared that this book is not completely accurate. I believe it is a work of daring exploration into little known territory.
In other words, you can't believe for sure EVERYTHING in it. But it gives some speculation for research. The authors have also
written a book on the hidden Jews of New Mexico (the original Spanish settlers 400 years ago), and they have researched the Melungeons,
who were those Scotsmen who married Indians in the US South. I forget the authors' names, but they got together when they discovered
they were of Melungeon descent.
I do not remember if they identify "Coleman" as Jewish. I would hazard a guess on "Coleman" that it is a composite of "Colum" or
"Colin", which may be a Celtic name, plus the Anglo-Saxon suffix "man," so the name means "man of Colum". I don't know if that is
Jewish, sorry. But names go through so many perambulations that it is often hard to tell where they came from, and historical records
It's interesting that the ancient Hebrews traced descent, as you say, through the father's side, while modern Jews trace through the
mother's. My deceased husband, who had a Jewish father, would then be considered Jewish in ancient times, although not in modern
times, for he had a blond German mother whose family came from Prussia to Ripon, Wisconsin. HIs name was Strauss, and his
maternal grandmother was Harriet Levi, so he was a "Levi-Strauss" like the "bluejeans" makers.
Sorry I can't further identify Coleman, but I would look under "Collins' if you start researching this. Happy rabbit trails! (I love rabbits)