What would cause the hostname FQDN to repeat the suffix twice?

What would cause the hostname FQDN to repeat the suffix twice?

I have three new CentOS 6 servers that connect to a DHCP server to get an
IP and to have DNS/rDNS setup to bind their FQDN and IP.
Two of them are behaving as expected.
One of them is appending the suffix twice.
Instead of fulton.mydomain.com we get fulton.mydomain.com.mydomain.com as
the FQDN.
This is not coming from /etc/sysconfig/network:
[root@fulton ~]# cat /etc/sysconfig/network
NETWORKING=yes
HOSTNAME=fulton
[root@fulton ~]#
On the other two systems /etc/sysconfig/network also just has the single
names.
This is acting as if the main name is "fulton.mydomain.com" which then has
mydomain.com appended again.
I cannot figure out if machine "fulton" is reporting its name to DHCP as
fulton.mydomain.com when it should be just using fulton or if something in
the DHCP server is causing this.
I cannot find anywhere on fulton where the fulton.mydomain.com is
specified instead of just fulton.
The /etc/hosts file on all machines is completely generic:
[root@fulton etc]# cat /etc/hosts
127.0.0.1 localhost localhost.localdomain localhost4
localhost4.localdomain4
::1 localhost localhost.localdomain localhost6
localhost6.localdomain6
On the DHCP / DNS server system, the only mention of these systems is in:
/var/lib/named/dyn/mydomain.com.zone
/var/lib/named/dyn/10.0.zone
Thanks, Laurence Brevard San Jose, CA
Adding various hostname outputs and sysconfig/network
[root@fulton sysconfig]# hostname -v -f
gethostname()=`fulton.home.rcousins.com'
Resolving `fulton.home.rcousins.com' ...
Result: h_name=`fulton.home.rcousins.com.home.rcousins.com'
Result: h_addr_list=`10.0.5.223'
fulton.home.rcousins.com.home.rcousins.com
See above - OOPS
[root@fulton sysconfig]# hostname
fulton.home.rcousins.com
PRETTY SURE ABOVE SHOULD JUST BE: fulton
[root@fulton sysconfig]# hostname -s
fulton
SHORT NAME ABOVE IS CORRECT
[root@fulton sysconfig]# cat network /etc/sysconfig
NETWORKING=yes
HOSTNAME=fulton
AND ABOVE IS CORRECT