Hide Event Details Within a Specific Layer
The Content Visibility settings in your timeline's appearance settings control whether event names, dates, and durations show on the timeline. They apply to every event, and there is no layer-level version of them.
To hide one of those details for the events in a single layer, open each of that layer's events, expand More Options in the event dialog, and check Hide name, Hide dates, or Hide duration under Content Visibility.
That way you can show a detail in some layers but not others:

These checkboxes only change what the timeline itself shows. The event popup and the event list below the timeline follow the Display in Popup & Event List settings instead, so a hidden date will still appear there unless you uncheck Dates in that section, which hides dates for every event.
To hide a whole layer, including its name and every event in it, see Hide a Layer.