OK, it turns out that I had to edit both the /etc/hosts amd /etc/sysconfig/network files. At first I simply edited the network file and the name shown on the login screen did change to Merovingian, but then when I loaded Gnome I got a warning that Gnome didn't have a network address for Merovingian so some programs may not function correctly. I had looked in the hosts file and seen that it looked like 127.0.0.1 was being assigned to localhost, so I just used the same format to assign 127.0.0.1 to Merovingian and everything seems to work now. Below are posts of these files. Please let me know if they look correct.
The /etc/hosts file:
# Do not remove the following line, or various programs
# that require network functionality will fail.
127.0.0.1 localhost.localdomain localhost
127.0.0.1 localhost.localdomain Merovingian
The /etc/sysconfig/network file:
Thanks in advance for anymore advice!!!