For markers in the Event Browser, you can hover your mouse over those and see your marker info. Simply enable View>Browser>Skimmer Info.
If you assigned custom names for those markers, you can then search them using the search bar above the Event Browser.
You can create a Smart Collection that filters on markers by doing File>New>Smart Collection, name it, then double-click on that in the sidebar to enter the smart collection criteria. Press the + key and assign “Markers”. Thereafter clicking on that Smart Collection will show all clips in the Event Browse containing markers.
To create a library-wide smart collection (IOW one that searches through all events in the library, not just the current event), select the library in the sidebar, then do File>New>Library Smart Collection.
If you toggle to List View (OPT+CMD+2), the Event Browser will show more info about each clip. If you press OPT while spinning down the disclosure triangle by the event name, it will unfold all ratings and markers on all clips. You can then scroll down and see all your marker names.
If you have many clips without markers, just use your marker smart collection to filter only on markers. Then with the Event Browser in List View, you can see the distilled version of clips only containing your markers and read the names.