for the actor, it's easy.
make an empty message with the new name as a title. you can use text replacement in this too.
then make an alias, set it to "stores text" and select your message in your dropdown.
once you've filled the alias with your dog, it's display name will be the new one.
for more names make more aliasses (forced optional)
"clears name if removed" if you want the dog to be back to normal name when back out of the alias
for locations, i've tried to do this for my lund+lambda mod, but totally failed.
either it's not possible for locations (no name selection for them also), or i'm too dumb.
they (loc aliasses) DO have the name replacement field that also can be filled in tes5edit though, but ck clears that back out, no idea what to make of this.
what you CAN do though is in doors that teleport to that location, select a new name they show for activation
for this you also make a message with the new name, but don't need an alias, just select it in the door ref teleport tab