For a simple set up, you have the right idea. You only need fine tune your layout design slightly:
Set up the Object ID field as a Pop up menu and set the value list to only show object names. Remove the object name field from your layout. Your Object ID field will now automatically display the Object Name even though it stores an ID number.
If you want a drop down list, Take the Object Name field and use the Inspector's behavior settings to deny browse mode access. Give it an opaque fill color and put it on top of the ObjectID field--which is formatted as a drop down list with the value list you have already described. When the user clicks on the object name field, the drop down list in the ObjectID field hidden behind it will pop to the front and deploy for selecting an object. When you select an object in this drop down, the list disappears back behind the name field which now displays the name of the selected object.
That will work for me. Thanks!