How to enable search when using Emoji keyboard on iPhone?
You can't use search when looking for emoji in the stock iOS keyboard.

iOS uses predictive text to determine what emoji to offer you based on the words you're typing.  While this isn't what you're asking for, you can see this iPhoneLife article for more info.

To search by emoji, you need to install and use a 3rd-party keyboard.  Many developers offer keyboards that incorporate emoji search.  I use SwiftKey (not associated with the software or developer) for typing on all my iOS devices.



Apple has indicated that the upcoming iOS 13 will offer:


  Word and emoji suggestions
  
  If you need to correct a word, simply ask and you’ll be presented with a list of suggested replacements.