Bassam

On a basic level, yes, it does mean "smiling", that being the adjective, not the verb (e.g. A smiling man). However, it has the weight of "فعال" which indicates exaggeration, extremity, etc. Thus, Bassam means someone who smiles a lot. "Basim" on the other hand is basic, meaning "smiling" or "smiler".

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Fun fact, "Bassam" is the dubbed name of Hyuuga Kojiro of the Captain Tsubasa series.

Actually, it means "smiler". It is the noun derived from the verb "to smile".