I suggest that you spend the up-front money to consult with a lawyer. A lot of them will do an initial meeting for relatively little. They will be able to give you some idea of what risk, if any is involved in this. Then you can make a better informed decision about whether to ignore this, fight, or conceded and change the name.
I find out a few years ago that there are whole law firms out there who basically just send threatening letters for low fixed fees. They don’t litigate or even provide real legal advice. It’s one step above selling pages of their letterhead.
You won’t know how serious these people are, or how serious their complaint is, without consulting a lawyer.
Best of luck!
I don’t really believe you, but I head that beautiful could get away with just being ornamental.