My mothers name was different on her birth certificate to the one that she got married under because her parents were not married when she was born . She always went by her fathers name although his name was not on her certificate. Does this mean that she was not legally married to my father because whenn she married she used the name she had grown up with not the one on her birth certificate?

If you explain what the real issue is here, aside from the different name, we can help and it will probably cut a few corners in back and forth questions and answers.

I don't think the name issue makes any difference to day to day activities, but may to others, so please explain so an expert can help you.

The fact that your mother married using a different name than the name written on her birth certificate does not invalidate her marriage. It is perfectly legal to go by a different name as long is it is not done for fraudulent purposes. She was married.