When layers are published to ArcGIS Online, the display field is unchangeable unless you overwrite the data. There has been mention of some workaround using the JSON and rest service admin tools but that has not worked for me.
The issue with the defined display field is that this carries over to editing in ArcGIS Online Map Viewer, Field Maps, Instant Apps, etc. and anything that uses the 4.x Smart Forms capability. When you click in an area that contains multiple points or potentially overlapping points, the display field is shown and there is no other way to change it than to overwrite and republish the data.
It would be helpful to allow this change once the feature layer has been published and is hosted in AGOL.