Be aware that there are lots of scammers around who make untrue threats to make you pay money. There might be hundreds of developers who got a very similar email from the same person.
It is very, very unlikely that the title of an app would constitute copyright infringement. Trademark violation perhaps, but not copyright infringement. Even if it did, the normal steps would be send a DMCA notice to Apple, and then either be happy that your app is gone, or to sue you. Asking for payment seems very dodgy.
I would first make sure that there is a legitimate business asking for money, with a legitimate copyright. Preferably a business older than the title of the app. And there must be no payment unless you get a written statement of which copyright they own (so you can sue them for fraud if they are lying), and a guarantee that there will be no further action. "Pay me or I take you to court" alone means they can still take you to court after paying.
Also remember that "copyright" is about the right to copy. If you use the same application name as somebody else by coincidence, that's not copying. For copyright infringement, you must have actually copied something. (Of course you can be sued and lose if someone convinces a judge that you copied, even if you didn't).