Locality name appears as total city for school district tax in box 20? Shouldn't it be, Troy,ohio?

[Hal_Al]

You need to ask your employer and/or check your pay stubs for which cities and/or school district the withholding was for.

The term "total city' usually means the employer withheld for more than one city.

Ohio has both city income tax and School District (SD) income tax (SDIT). Boxes 18-20 are used for either. The use of the term "total city" tells me your's is city not SD.

 You normally only have to file a return in the city you live in. It is not necessary to file one in the city you work in, if different. Your employer will remit withholding to the city you work in, but you do not file a return unless you're claiming a refund or your employer didn't withhold enough ( both highly unusual). The city you live in will allow a credit or partial credit for the withheld tax you paid to the work location city. 

Employers are only required to withhold for the work city, although many will voluntarily withhold for the resident city as well.