Profile fields marked as "searchable" will be available for all people who are logged in 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 "People can hide real names" and "Search usernames" as well as individual preferences.
Other searchable profile fields listed here such as email address can be used to find people in a search query, but they are not displayed in search results.