The names of your layers, superkeys and macros are not stored on the keyboard to save memory.
However, from 1.3.8 onwards, Bazecor saves and restores the names of layers, macros, and superkeys on backups.
If you sync your backups with something like Google Drive or similar, you can restore them on your different devices, and your names will be restored, too.
You can find and restore your backups in the Preferences menu.