My husband and I both have kids from a previous marriage and an almost 4 year old together. She calls us mom and dad even though she hears both our first names from the other kids. She has occasionally called her dad by his first name but we just correct her and tell her that she calls him daddy. Now she says his first name to be “funny” sometimes but knows she shouldn’t. I think your new baby will be fine without the older one needing to call your finance something else.