Bonar \b(o)-nar\ as a boy's name is of Old French origin, and the meaning of Bonar is "gentle, mannerly". From the French word "debonair". In English, "debonair" now means something closer to "nonchalant" or "urbane", as personified by Fred Astaire. British politician Bonar Law.
Bonar has 2 variant forms: Bonnar and Bonner.
A baby name that sounds like Bonar is Banner.