Can I rename the "Pictures" folder without "Full Disk Access"?
If you want to do this as a regular user running in standard mode, then no - you have to ask the user to grant permission via Full Disk Access.

You can do it through other means by booting the Mac in Recovery mode for example, but I assume this is not something you want to do as part of a standard process. Granting the correct permissions is way easier.

Note that it is possible to grant the permission, make the change, and then remove the permissions again. This will help if you feel that it is too permissive to allow this software Full Disk Access forever.