it’s certainly not the norm to call parents by thier first names in a loving way, but there’s no reason it has to stay that way. Most people don’t use nicknames for their best friends, siblings, some people even use first names with their spouses, and that doesn’t mean these people are loved any less. using first names isn’t inherently distant/cold.
but at the end of the day honestly I think what you call your loved ones isn’t that important so if you’re more comfortable using mom/dad, that’s ok too