You will not be able to change the names of the fields when doing a search.
In EndNote you can customize any of the 54 fields of a Reference in any of the 53 Reference Types. So for the 53 Reference Types a field could have 54 different names.
So when doing a search EndNote will display the Default Name of the field because otherwsie EndNote would not know which name to use.
If you would like to see this feature changed in a future version of EndNote, You may want to submit a request for a product enhancement on our website.
http://community.thomsonreuters.com/t5/EndNote-Product-Suggestions/bd-p/en-suggest