I just now got the pun! Olive the Other Reindeer = "All of the other reindeer"! I admit I'm slow!
SPOILER ALERT***** That's actually the plot of the show. She hears "All of the other reindeer" on the radio, and thinks Santa said "Olive, the other reindeer." Round John Virgin and Richard Stands (from which it stands...) also appear in the special.