Please use FileMaker Server Software! It makes your setup much more stable and allows automatic backups.
For a first test use the cheap version you can get here if subscribing as developer.
confirm you are using two different license keys. Confirm you are not having local name, IPv4 and IPv6 conflicts.
Out of curiosity, is the software registered to "Myself". Where would it get that from?
As Jens said, using the software as recommended with FileMaker Server will solve all of these types of problems. But it does mean purchasing a FileMaker Server license.
I agree with bigtom that it may be how your computer is connected to the network and broadcasts itself.