Can I notify a single user for some alerts?

Notifying a single user with OpsGenie is straight forward; just specify the user as the recipient of the alert. 

If you are using OpsGenie Alert API or tools (lamp) to create alerts, you can put the username of the user into the recipients field. If you're forwarding alerts to OpsGenie via email, you can define an email rule and specify the recipient there.

Example: 

Note that if you're creating the alerts via the web UI, OpsGenie web UI allows entering user's full name and auto-completes as you type in the name. It actually sets the recipient to the username in the background.