Profile fields marked as "searchable" will be available for all logged-in users to search on.
First name, last name and display name are generally always searchable. However, the exact behaviour of name searches is controlled by the settings on the site options page for "Users can hide real names" and "Search usernames", as well as individual user preferences.
Other searchable profile fields listed here such as email address can be used to find users in a search query, but they are not displayed in search resuts.