Adjusting the Contact selection display (e.g. New Contribution)
You can, from the menu: 

Administer > Customize Data and Screens > Search Preferences.

The setting to adjust is Autocomplete Contact Search.  There are a number of choices you could include.  This doesn't impact the field in question only though.  The biggest additional impact would be the Quick Search.  Note the help text: 


  Selected fields will be displayed in back-office autocomplete dropdown
  search results (Quick Search, etc.). Contact Name is always included.




The next option down on Search Preferences (Contact Reference Options) may come into play for certain fields as well.  Its help text:


  Selected fields will be displayed in autocomplete dropdown search results for 'Contact Reference' custom fields. Contact Name is always included.