As Starblaze said, "Its just a name OP. You owe an apology as you have caused this issue, not the name." and I agree.
Everyone has a right to feelings/opinions but what you do with those 'things' is what matters.
Also, some seem to forget that if You have a thought/opinion on something and express 'it' to others', THEY have "same right" to disagree and have an opinion about what you said.
The moral of the story being, if you express a dislike for something that was NOYB (like their child's name) and the person who it IS "their business" objects to your opinion/view, then you need to own up and apologize.
Family rifts/resentments tend to build over time and focusing on the 'name' of the child and not the child itself is such a waste of energy.