The phrase "to complete a profile" means to provide all the necessary information or details about yourself or something in order to have a comprehensive or full representation. Full definition
They not only perform searches for you, they'll also complete your profile for you and provide you with a lot of other premium and personalized services. (millionairematchmakers.us)
Their Online personals include complete profiles with photos, searches and profile browsing and anonymous email messaging to other members. (prweb.com)
Sometimes the most challenging part of completing a profile on dating sites is having to write a personal ad. (uk.match.com)