You can (or could?) place collect calls in the US. The receiver of such a call then pays the bill. To prevent abuse, you give your name and then the phone operator will ask the receiver "do you want to accept, and pay for, this collect call from Bob Smith?"
The video is just making fun of that situation by encoding a message in the name.
Students also frequently had shared phone services of various types so they'd make a person to person call to their parents with some agreed-upon name and their parents would call back at the shared number. When I went to school we also traded cassettes because phone calls of any length were expensive in any case.
(The context is that long distance phone calls cost maybe $4+ per minute in today's dollars.)
The video is just making fun of that situation by encoding a message in the name.