And I speak as the child of a disabled father. I did harbour a resentment that I had to be his caregiver (I was until he passed away BTW). I'm fairly certain that was the reason I have never married or had kids, I was 'otherwise' occupied and couldn't date, or anything that would lead to a relationship.
but you could have had a father who wasn't disabled at the time you were born and still wound up being a carer for him later in life and that happens to many people.
And similar things can happen even when the parent(s) aren't disable. They could be alcholics, drug users, problem gamblers or plans simple lazy bastards.
People with disabilities want to have kids for the same reason other people do - the maternal instinct but I wouldn't say they are driven to have kids.
Of the people I know with disabilities (including my wife) I can't say any of them were dead keen to have kids though one (she has spina bifida) recently had a baby girl but that wasn't planned. However she doesn't want some-one to raise the baby she wants to do that herself with the help of her boyfriend.
As to the actual subject, the family name for my paternal grandfather and father will come to end and with my generation.
There were 4 kids in my family (two of each), my sisters married and took their now ex-husbands names. My wife and I don't want kids (I don''t really have the patience for it) and my brother I'm not sure.
My grandfather was the youngest of five. He and his brother had daughters (my mum had two brothers by they died in infancy) who took their husbands name, the sisters had sons.