The names of your layers, superkeys, and macros are not stored on the keyboard. This is to save memory for other features.
However, Bazecor saves the names of layers, macros, and superkeys on backups.
If you sync your backups with something like Google Drive or similar, you can restore your latest backup on your different devices, and your names will be restored, too.
You can export and load your backups under Preferences > Backups.
If your Bazecor doesn't look anything like that, you have an older version. Please download the latest Bazecor Version here.