Hope all is well.
I have a 2nd great grandmother named Theresia Starr 1860-1938 (Star, Starr, Stahr, etc etc) in my family whose father is listed as John Starr (mother as "unkown")from Germany on her death certificate. Family stories say she was adopted through a local church here in Cincinnati, Hamilton, Ohio; though the same document says she was born in Green Township (a suburb of Cincinnati). Other stories say she has Cherokee Indian in her.
Of course this means that ::someone:: knew her father's name and was able to tell the Hamilton County Department of Health so that it appears on her document.
We have plenty of census forms placing her in the area which generally agree on her age. She married Andrew Lipps, Jr. in 1884 and had a number of children, a few of which are alive today. I have pictures of her and Andrew together. I'd be more than happy to exchange info with you to see if our Starrs are the same people.
Let me know.