I had 5 droids that I picked up which had custom images, but I didn't have enough room for them, so I had to repackage them to be able to load them on my ship. When I unpacked them again, both their custom images and their names were gone. Was that supposed to happen?
Yes. Because of the way crating works, it deletes the items and creates new ones when you unpack. Since custom images are linked to id and the droids now have a new id, they no longer have a custom image. It is just unfortunate.
I may be wrong, but I thought this was fixed some time ago (a year or more). I never tried it myself but I have the memory of a sim news saying that packaging and repackaging items would not cause custom images to be deleted.. or bay it just works for items and not droids.
Repackaging actually deletes the physical item, as opposed to storing the item inside something. This helps keep those 500 bacta patches from overloading the travel screen, scanners, db etc. So when the item is deleted its corresponding ID is also deleted. hence the loss of the custom, as they are linked via ID.