Hey Deb, I did a little research and he did live there but it isn't named after him. It was named in 1801 after a Colonel Zane.
From the towns web site...
In the 1790s, a settlement was established at the confluence of the Licking and Muskingum Rivers as Colonel Ebenezer Zane and his son-in-law John McIntire blazed Zane's Trace, the original pioneer trail into the old Northwest Territory. Zane, a Revolutionary War veteran, was commissioned by the U.S. Congress to blaze a pathway into the rolling hills and the dense forests of the Ohio Valley, and to establish ferry crossings at three major rivers including the Muskingum.
McIntire and Zane's brother Jonathan took responsibility for operating the ferry at the Muskingum River and they were the county's first settlers. A town laid out by McIntire called Westbourne quickly grew out of the settlement and in 1801 it was renamed Zanesville in honor of Colonel Zane.
Thank you for the info. What a coincidence Zane Grey lived there. I was only joking. I believe he lived for a while in Port Jervis NY where that diner with the apple pie is. There is the Zane Grey Museum. Wanna go???