Step daddy vs. daddy

So my daughter calls her step dad “daddy” but her real dad “baybay.”

Real dad has a problem with it which but my daughter started it on her own. (She’s about to be 4)

She’s only seen her real dad 10 hours out of the last 2 years.

He sometimes sends her money but is not on child support...

My husband pays my daughters dental care, insurance, daycare and we provide just about everything for her...

Real dad told me I should correct her but I don’t want her to feel like an outcast since we call him daddy because we have a child together also...

Should I correct her and tell her she’s not allowed to call him daddy?

If not what do I tell her real dad?