The search results are based on the information you have included in your profile.
The more details Facebook has about you, the more fine-tuned their search will become.
Their profile will only appear if the email address you typed is the one they have associated with their Facebook account.
If this person is a new or long-lost friend, or someone who you haven’t seen in a while, it is considered polite to send them a message along with your request. Help them remember who you are, so they don’t deny the request by mistake.
You may want to browse this list for friends you didn’t think of in your original search. You can also use this list if you can’t remember someone’s name.
For example, if you use Gmail, you will be required to log in to your Gmail account, click on “Export” within Gmail, and select the contacts you want uploaded to Facebook.
You can take the opportunity to invite them to join you on Facebook.
Type your friend’s number or email into the search box and Facebook will send them a notification that you have requested their presence on Facebook. To invite multiple friends at once, place a comma after each email address or phone number.