This is a feature that appears to have been added to the latest firmware. It's the Display Name setting.
In the last case, above, you're probably on the Trinity Chorus preset. By default, the Display Name setting is set to Auto, displaying a selected Model name for 3 seconds, then returning to the current Preset name. Changing to Model in the Settings / Display Name screen will change the behavior to always display the Model name.
Access Settings by holding the Effect knob down for 1 second. You can then scroll through the various HX One settings with the left/right arrows, with the Display Name setting as the last one.
