Like, if you have two dads, but need the attention of one specifically, do you say “Dad Jeff!” to get Jeff’s attention or “Dad Carl!” to get the other one’s attention?
Or if you have two moms, and you’re talking to a third person about one of them, do you say “Mom Kate…” and “Mom Beth…”
I have heard some kids have different names for each - for instance, one would be “dad” and the other would be “poppa” (papa?) - or one would be “mom” and the other “mama”.
It’s handled by each family individually. I suspect the most common, and the method I will probably take if I ever have kids, is to use two different forms: Ma and mom or dad and daddy.
I would suspect that the answers are as varied as the families you’re talking about.
Some clues might come from the ways that people deal with multiple living grandparents and options could include:
My friends are “Mummy Name” and “Mummy Name”. But the kid can’t talk yet and he may end up naming them himself. My kids call their grandparents “Granny and Grampa” as we taught them but my elder niece called them NitNit and Papa and it stuck and passed to the younger niece too.
In all the families I’ve seen personally, the kid just says dad or mom, and if the wrong one responds it’s like, “No, the other one!” But mostly it works.
I’ll start paying better attention though.
I imagine it’s pretty similar to families where both sets of grandparents are around a lot (so, lots of different answers).
For me, I had “grandma” and “gram.”
One couple I know, it’s Mommy and Mutti. It helps that Mutti is actually German.
Another couple decided to go with Daddy and Papa. But the little girl insists on Daddy and Daddy. What are you going do, right? Daddy and Daddy it is.
My sister’s family has “Mom Fran” and “Mother Mary.”
Guess we know which one is responsible for going to the kid in times of trouble, mm?
And, yeah, even straight couples have lots of different options (Mom and Dad, Mother and Father, Mamma and Papa, Mom and Pop, Ma and Pa, Ma and Da, Mommy and Daddy, etc), so there’s plenty of options to draw from even before appending the parents’ first names, or borrowing from another language (another possibility I’ve never seen personally, but have heard of).
I assume the latter is the one that’s planning on coming to them in times of trouble?
Let it be, guys, let it be.
I’m fond of the plural form I’ve heard used. Instead of “Mom and Dad went to the store” it’s “Moms went to the store/Dads went to the store.”
“Dad and Papa went to the store” works too.
I’ve heard of several families headed by two gay men, where one parent is called Papa and the other Daddy.
I’ll be fine with whatever my child wants to call me and my (hopefully one day) husband. Dad is my personal favorite (it’s what I call my father). But if my child wants to call me Drew, I’m cool with that too :D, haha. Uh oh. Does that make me a hippy? 
Our kid just calls us “meow”. But then, that’s about all he says.
Well, that’s what I and my younger brother did to distinguish between my grandparents; so I’m sure that at least one gay/lesbian family has come up with the same solution.
One that I’ve heard that I’m not particularly fond of, but don’t have any kind of dog in the fight so I just kept my mouth shut, is that in the town where I grew up, kids with two moms have taken to calling bio-mom some form of traditional “mom,” “mommy,” etc., and their other mom, auntie.
I assume she’s wise as well.
I don’t mean to alarm you, but your child might be a kitten.