Nokia 2320 Classic - Can I remove the time or date from home screen on my Nokia phone? (Series 40)

Yes.

To remove the date, select Menu > Settings > Date and time > Date and time format (or Date and time format settings) > Date > Date on standby scr. (or Date in Home screen) > Hide date (or Hidden). To remove the time, select Menu > Settings > Date and time > Date and time format (or Date and time format settings) > Time > Clock > Hide clock (or Hidden).

Or, in some touch screen phone, to remove the date and time from home screen, select Menu > Settings > Display > Home screen > Personalise view > Clock > (empty) or other desired options. You can still see the time at the upper right corner on the home screen.