User picker should match typed name on the concatenation of first name and last name as well

Consider the following use case:
I have a user with username lucaa and first name Anca and last name Luca.
I am trying to select this user with a standard user picker on a field in an application.
If I type "Luca", I will find the user, whose display name is "Anca Luca". If I type "Anca" I will find the user, whose display name is "Anca Luca". If I type "Anca Luca", I won't have any result.

This issue can become blocker on wikis which have a lot of users, where typing a first name will bring up a lot of results, typing a last name can also bring up a lot of results (e.g. if the last name is a common prefix for many other last names), knowing that the number of results that we show to the user is limited. There would be no way to search in order to be sure that we can find the actual user of a person.