Rainbow Dash's dad is named Rainbow Blaze, though as you point out it's unclear if them sharing names is a convention or just because it's an obvious trait of both of them.And of course we know practically zip about Rainbow Dash's and Fluttershy's families. Although how Rainbow Dash got the first half of her name looks pretty obvious.
Although being a (formerly) militarized society, my personal head canon is that Pegasus society as a whole doesn't have nuclear families like Earth Ponies and Unicorns do, and that Pegasi children are communally raised with biological parents taking more a "big brother/sister" role if they're interested. Not that there aren't Pegasi nuclear families, but those tend to be made up of Pegasi who grew up in Earth Pony and/or Unicorn communities. It would explain why we never hear about Rainbow Dash's and Fluttershy's families; they functionally don't exist in Cloudsdale.