It sounds like your dad created a new account. Changing the computer name itself would have no effect on access to drives files & folders. But logging in under a new/different account would, because files & folders are normally secured to the account that created them.
Since the pictures are on an external hard drive, you can tell OS X to ignore permissions on the external drive. Using the Finder, select the external drive, then do GetInfo (File > Get Info). In the window that opens, open the "Sharing & Permissions" area. Check "Ignore ownership on this volume." After doing so, all accounts on your Mac should be able to access the files & folders on your external hard drive.
Is your dad using iPhoto or Aperture for his photo library? I ask this, because both of those programs embed the disk name in the library entries, and if the disk name is changed, it won't let you access the full resolution picture until you correct it. I remember it is very easy in Aperture, but I don't remember how to correct it in iPhoto. I had this happen to me a while back and I ended up correcting it in Aperture, which corrected the iPhoto entries because the two libraries are connected with the most recent updates.
The more I think about it, it sounds like MartinR has the correct suggestion for you.