Welcome to iMore! I would first make sure you have created a contact card for yourself. Include your number and email. Then go to Settings > Contacts> Tap on "my info". Then tap on your contact card.
If search still doesn't work, try a hard reset.
You don't say which phone you use.
If the reboot doesn't work, try Reset All Settings.
Reset All Settings
Go to Settings >General >Reset >Reset All Settings. This resets to default everything in Settings, including notifications, alerts, brightness, and clock settings like wake up alarms.