(not a teacher, just a native speaker)
Aside from the obvious tense of the verb difference, in meaning I think that "He heard someone calling his name" would seem they might be calling his name over and over, as if they were trying to get his attention. If you were in a classroom and the teacher was trying to figure out who Jane Smith is, she might repeat the name over and over. Jane's friend would say, hey, the teacher is calling your name.
The other, "call his name" tends to indicate more that somebody called it out once. Again say in a classroom, the teacher reads a list of names once. Jane says, "I heard you call my name."
best of luck