New domain name
 

Let's say that you decided to buy some brand name, and have discovered that your domain .com is available, but when you search in google for that brand name, you find some music artist that is selling songs but doesn't own domain .com

Would there be everything alright if you have the same brand name for porn?

It wont cause any problem but a nice advertising to both of you IMHO.
If it's a rock band - there won't be problem at all - porn and rock can do nice partnership....

But if it is gospel singer or opera star, or a child song artist well... you can try selling the dot com to him for a big profit if he's famous.

From what I always understood (I could very well be wrong) of they own the trademark/copyright/whatever to the name after you buy it they can sue you and take the name etc. but if they get a copyright afterwards or don't have one then there isnt too much they can do about it.

Again, I am not very knowledgeable in this, thats just what I have been told in the past about domain names in general.

Best of luck with it.