When in F7T2, the terminal prompt lists my computer as localhost, even though I gave it a name during install.
[root@localhost ~]#

When in F7T1, it lists my computer as F7T1, the name I gave it when installing from DVD.
[root@f7t1] ~]#

The /etc/hosts files have the same form:
[root@localhost ~]# diff /etc/hosts /mnt/f7t1/etc/hosts
3c3
< 127.0.0.1     f7t2.thetoolshed.us     f7t2    localhost.localdomain   localhost
---
> 127.0.0.1     f7t1.thetoolshed.us     f7t1    localhost.localdomain    localhost

This naming persists, even though I set hostname with the hostname command.

The next time I boot to f7t2, the hostname is back to "localhost"
[root@localhost ~]# hostname
localhost
[root@localhost ~]# hostname f7t2.thetoolshed.us
[root@localhost ~]# hostname
f7t2.thetoolshed.us

In f7t1:
[root@f7t1 ~]# hostname
f7t1.thetoolshed.us

Here are the /etc/sysconfig/network file contents:
[root@localhost ~]# cat /etc/sysconfig/network
NETWORKING=yes
yesHOSTNAME=f7t2.thetoolshed.us
[root@localhost ~]# cat /mnt/f7t1/etc/sysconfig/network
HOSTNAME=f7t1.thetoolshed.us
NETWORKING=yes
yesHOSTNAME=f7t1.thetoolshed.us

There was a bug in F7t1 anaconda (bugzilla #227250) that didn't honor the host name set by the user; is that still the problem?  Or, is there something I'm forgetting to do?   I added this comment to the bug report.

In this case, removing the yes from yesHOSTNAME and restarting the network does not solve the naming problem.
[root@localhost ~]# service network restart
Shutting down interface eth0:                              [  OK  ]
Shutting down loopback interface:                          [  OK  ]
Bringing up loopback interface:                            [  OK  ]
Bringing up interface eth0: 
Determining IP information for eth0... done.
                                                           [  OK  ]
[root@localhost ~]#

Gerry