Would you please have a look at these sentences? Are they correct?
1) What a horrible song!
2) What awful news!
3) What beautiful music they are playing!
4) What fun your friend Maisie is!
5) What a strange name to give a dog!
6) What good meat this is!
These are all correct although I would not place an exclamation mark on all of them. Phrases like "What a strange name to give a dog" *can* have an exclamation, but a lot of people tend to overuse the exclamation point. You should try to reserve the exclamation point for things that truly are shocking. Your sentence "What horrible music!" was a good choice.
I'm not saying that you can't be shocked by a dog's name, I'm just saying you should use the exclamation mark very judiciously.
Treat it the same way you would treat screaming in public. Essentially that's what you're doing. :)
I guess what I am saying in short is, all of these sentences are technically correct, the usage of the exclamation point is really based on context. Use your best judgement :)