I don't find it strange or off-putting to see names of any descent (Jewish, Arabic, Japanese, French, whatever) used in families with no link to that heritage. It is done every day and it should be done, in my opinion. No heritage has the sole right to use a name over any other.
Solomon used to be a favorite of mine. It has this exotic, strong feeling to it that I really love. Sol is a nice nickname for it. I also like Solo (SAUL-o).