The participant search logic works based on how the value is started. This value is stored as a single value in Luminate Online, so if you utilize spaces in the screen name it will require users to search for the first part of the screen name or search for the entire screen name.
 

Example: Screen Name- 'Taco Tuesday' would be found with a search for 'Taco', 'Tac', 'Taco Tu', but would not be found by searching 'Tuesday'

It was determined searching for partial screen names could create a large amount of unrelated search terms, so a product decision was made to only use the start of the screen name to find results.  At this time there is not an option to modify the built in search logic.