Please Help missing backups

intel core duo 2 lion 10.7.5
This is my iMac and I have recently set up a slave BT home hub for wireless at the other end of the house and also just moved my iTunes library to an external hard drive which is the same hard drive as my time machine uses.
I went to find some files in time machine, and I only have back ups to the 4th nov, previously I had maybe a years worth. My back ups are now labeled like this Adam Butters iMac (2)
and time machine looks like there are other backups but I can't access them please help me someone

 

more info

Ok so my computer was given another name by my router and so time machine has started to make back ups under this new name but where are the old back ups I have not agreed to delete anything???