Here is a reasonable interpretation. The verb "to mumble" means to speak quietly and not clearly, so that what you say is hard to hear or understand. The noun "mumble" means something which is quietly and indistinctly spoken. The three men were introduced to the speaker and the two girls. I believe that whoever introduced the three men mumbled their names, so that the speaker does not know their real names. All he heard was an indistinct sound -- a mumble. So for humor's sake, he uses the word "Mumble" in place of their real names that he doesn't know.

Mumble means not to speak clearly. When one mumbles, they talk as if their mouth were filled with marbles.