I am able to ssh to a machine on the LAN using either host name (my router has dnsmasq turned on) or IP. That works just fine.
My confusion started when I took a machine called lapdog2 which used to dual boot Vista and Ubuntu (through several releases) with both named lapdog2. I would ssh into Ubuntu there with no problem.
I just replaced the hard drive and only installed ubuntu 12.10 and LinuxMint 14 as a dual boot (yes, it is a bit redundant but I had my reasons) and named them lapdog0 and lapdog1 respectively. I can still ssh by name or IP but ssh tells me every time that the host key for that IP differs from the one stored when it was lapdog2 (entry 8): It does not seem to tell me there is any difference for lapdog0 (entry 22) vs lapdog1 (entry 23):
larry@hammerhead:~$ ssh lapdog1
Warning: the ECDSA host key for 'lapdog1' differs from the key for the IP address '192.168.2.124'
Offending key for IP in /home/larry/.ssh/known_hosts:8
Matching host key in /home/larry/.ssh/known_hosts:23
Are you sure you want to continue connecting (yes/no)? yes
Welcome to Linux Mint 14 Nadia (GNU/Linux 3.5.0-17-generic i686)
Welcome to Linux Mint
* Documentation: http://www.linuxmint.com
Last login: Fri Nov 30 16:40:24 2012 from hammerhead.thiel.org
larry@lapdog1 ~ $ logout
Connection to lapdog1 closed.
larry@hammerhead:~$ ssh lapdog0
Warning: the ECDSA host key for 'lapdog0' differs from the key for the IP address '192.168.2.124'
Offending key for IP in /home/larry/.ssh/known_hosts:8
Matching host key in /home/larry/.ssh/known_hosts:22
Are you sure you want to continue connecting (yes/no)? yes
Welcome to Ubuntu 12.10 (GNU/Linux 3.5.0-18-generic i686)
* Documentation: https://help.ubuntu.com/
14 packages can be updated.
13 updates are security updates.
Last login: Fri Nov 30 16:21:16 2012 from hammerhead.thiel.org
larry@lapdog0:~$