You can search for people in many different ways including by first name, last name and full name. 

You can enter just the first letter of the first or last name and then sort by First Name or Last name by tapping on the funnel and selecting Sort.

Tip: Type "Help" in the search box for some search examples based on your contacts. 

Tap on the People section and then enter the person's First Name in the search box.

 

You can also search by Last Name.

 

And search by Full Name.