I have two SDs (2 & 6 when I moved in, 7 and 12 now.) They call me a pet name (that I've had since birth within my own family.) I also have a daughter aged 3.
They see their dad every other weekend for two nights.
The younger one has started referring to me as dad when talking to others - sometimes.
The older one never has, although we've talked about the nature of our relationship a lot as she likes to discuss things which I think is healthy.
Unfortunately as she's aged several challenges have shown themselves - ADHD, reduced learning capability, Dyscalculia, Dyslexia, impaired executive functions - a real cocktail. She frequently has meltdowns. This has tied up a lot of wife's time and meant that me, toddler and SD7 are together a lot. I don't really feel a great difference in my bond between my own daughter and her, and the two of them are really, really close (partners in crime would be my best description...)
Obviously if the three of us are playing, SD7 will refer to me as 'Dad' when talking to my daughter.
In other scenarios, when she's talking to other people, I think that she's testing the water - not confused by who is who at all, just pushing to make sure she won't get the rejection of "don't refer to me as that, don't call me that."
She's a middle child with a toddler sister and a SEN sister, which is hard enough already. I do respect her real dad but there isn't a fucking chance I'll correct her and risk causing even the smallest feeling of rejection or hurt. She doesn't remember me not being in her life.
Their dad finds it easier as the kids get older. I suspect over time she'll bond more strongly with him, and that's obviously great.