Not sure which android o/s version you have , BUT , if you try the following
pull down from top of screen.
press cogwheel ( that should get you in to settings )
i have a tab marked general ( lollypop version of android ) , select it.
If you click accounts it should show what accounts if any are on the phone.
It should have your google account ..... If not i would add it.
I would also set up wifi on the phone to allow faster download of apps and contacts etc.
It should then download all the contacts in your gmail account , including the peoples names and phone numbers.