This is normal behavior for a drop down list. A pop up menu may be configured to show only the second field value even after you exit the value list, but not for a drop down list.
There are tricks you can use to compensate for this with a drop down list. One method is to put the name field on top of the drop downlist formatted field and give it an opaque fill color so that it hides the drop down list field. Then use behavior settings in the inspector to deny browse mode access to this name field. When you click on the name field, you automatically click the field hidden behind it and this drop down list pops to the front and deploys.