The tsadikim gave the following reason for why he was called the Ba’al Shem:
“Ba’al” means a lord or ruler. Every ruler has his weapons through which he rules. The Ba’al Shem’s weapons were the souls that he drew to him as hasidim [=followers]. Soul means name [shem] as evidenced by the verse “[and whatsoever the man would call] every living creature [=nefesh], that was to be the name thereof [=shemo]” [Genesis 2:19]. So he is called Ba’al Shem because he is the lord and in charge of the souls of his men.
I.F.
Rabbi Kelemer
