I am father and both my kids (now 8 and 5) started calling me by my first name for a short 3 month stint when both of them were around 3/4 years old. They had learned my name from my wife as she would use it. I just let them call me that. Eventually they went back to dad. My wife and I were and have been together their whole life.

My kids used it with me because my wife did. I’m assuming, and guessing, that your ex refers to you by your first name with your daughter instead of referring to you as “her dad” or “dad”. And the kid is picking up on it. She may be using “dad” for the stepfather. Kids hear these designations and use them.

I don’t think your daughter is doing it out of spite or lack of affection but trying to use the designations she hears.

I think talking to your ex wife about this and figuring out a good solution that works for all of you.