[[WMG: Mary Richards is actually [[TheDickVanDykeShow Laura Petrie]],]]
who changed her name, after divorcing Rob, taking her son's first name "Richie" as her new fake last name. She did this because she wanted to start a career in the entertainment industry but her ex-husband was a famous television writer, and she was concerned that gossip about their messy divorce might hurt her career if people made the connection between them.
* Maybe this is obvious and you're basing you're theory off it but that's supposedly why the network made Mary single instead of divorced. They were concerned that viewers would think that she divorced Rob Petrie.