When we got married, SS, then 13, announced that he was going to start calling me mom. I told him that mom was a name for only one person, and since he has a mom, I'd prefer to be called by my name.  BM here was high conflict too. 
 

If she's just doing it accidentally, then let it go. If it's "accidentally on purpose", then I'd ask her to call you by name. 

My ex SD called me every name in the book but mom was not one of them. LOL

If there is a HCBM best to nip this in the bud as crown said. You dont need any future volcanos from BM, and to make it worse she may get mad at SD. SD sounds sweet and sees you as a mom figure, so I am sure you can figure a good name that suits you . I have a coworker who calls her step mom  in their first language they speak at home , maybe something like that. Would be less threatning.

I'd just let it go without comment.  None of my 3 SKs called me Mom but OSS57 now occasionally refers to me as Mom now that BM is dead.  Since they lived with us in a blended family situation, to the outside world I was the "mom".  They referred to me that way, it was kind of a shorthand when we didn't want to explain our situation.

I really have no problem with a Skid calling their SP Mom/Dad.  In that home, that is what the SP may be. The opposition gets zero say in it.

Now, to bare my hypocritical side... I used to call my XILs mom and dad.  Then I hit a point where I was just not okay with that any more at which point I started calling them by their names.

I have never referred to my incredible bride's parents by anything but their first names.

I have a great mom and dad and no one else  has or will ever fill those roles in my life.  My ILs, either set, never have so... I don't recognize an MIL or FIL as a parents... hence, they do not get called "mom" or "dad".

All that said, I was the first person my SS ever called dad(dy).  His choice.  So, Dad is who I am for him.  Interestingly, he has never called his BioDad "Dad" he has always called him "Daddy (Firstname)" when he was little and "FirstName" once he got older.  Again, his call.  It always chapped the SpermClan's asses, but.... SS was historically pretty confident in his choices on who his "Dad" is though he did struggle with their aversion to it when he was little.

Incident 1:  

SS: "Dad, (SpermGrandHag) says you are not my real dad. You are only my stepdad." 

Rags: "Son, we have talked about  how a BioDad is the dad that made you with your mom and how a StepDad is the dad who is married to your mom.  Now, a REAL dad is the dad who loves you and your mom very much, goes to work every day to work hard to provide a nice safe home for you to live in, good food to eat, a safe neighborhood to live in, the best schools to go to, safe reliable transportation to ride in, reads  you a bedtime story every night and tucks you in, teaches  you to use the potty, teaches you to read and write, teaches you to tie your shoes, teaches you to ride your bike, coaches your sports teams, and makes you and your mom the most important people in the world."

SS: "Dad, a StepDad sounds like a REAL dad to me. Can we go outside and play?"

Rags: "We sure can son."

Incident 2 about 5 years after the first incident:

SS: "Dad, Grandma (SpermGrandHag) says that you are not my REAL dad and I can't call you dad any more."

Rags: "Son, you chose to call me dad when you were 2yo.  If you are not going to call me dad any more that is up to you.  However, I do not allow children to just call me by my first name so, if I am not going to be "dad" any more you can call me Mr. Rags."

SS:  "I think I will stick with dad.  You have always been my dad and you are my dad."

Rags: "Sniffle sniffle and claim an eye allergy."

Happy tears.

Only you and the Skids can figure out what they will call you.  You are the one with the decisioning authority.  No one in the blended family opposition has shit to say about it.  Or at lease they shouldn't.  If they do, they should get the STFU message and told to back off and stay out of it.

IMHO of course.

If your SD is 12, not 3 or 4, her referring to you as "mom" is probably intentional on her part. Also, I'm sure she knows the fire storm it would cause if her BM knew she called you that, so I don't think that will be a problem. I would consider it a compliment and as a sign of love and acceptance, but only if you feel comfortable with it.My two SS's called me Mom K for a few months, and then just Mom. Their choice....I never mentioned it either way, their choice.

I took on my skids when they were very young (ie both 2 and under) and there was a point where they started calling me Mum. I tried to correct them and then they thought it was funny and kept doing it more so I ignored it. BM and her mother then found out and put an immediate stop to it. 

I personally think that if the bio Mum is active in the skids lives that it's disrespectful to her (not matter how much you might not like her) to allow your skids to call you Mum. My SS, whom I'm very close to, views me as his other mother but calls me by my name and that works for everyone. He sees himself as having three parents, DH, BM and me - he doesn't include BM's husband in that picture. SD16 probably has a lesser view of my position as I'm not as close to her. 

DH had full custody when SD was 5. She saw me way more than her actual Mom. SD started calling me Mom (I was indifferent), but then when BM found out, she put an immediate stop to it. Of course BM thought I was trying to "take her place" and was forcing SD to call me Mom. BM was even MORE furious when DH told her that it was all SDs idea because it was what made her comfortable. This is what sent her over the edge... that SD actually chose to try calling me Mom. 

Looking back, instead of being indifferent I should have told her no. But having full custody made it difficult to tell her no, when in reality I was doing ALL of the mom duties. 

You may very well be Mom.  Just because BM squeezed them out does not necessarily make her Mom.  Some honorifics are earned rather than granted by mere biological function.

My SS chose to point at me and call me Daddy when he was ~15mos old.  Kids are smart, many of them know full well who their REAL parents, regardless of who their BPs are.