Why is Stockport County so called when Stockport is not a county unlike Derby and Notts?

I have not been able to track it down but have found a Hatters history on https://en.wikipedia.org/wiki/Stockport_County_F.C.
The site has a contact e-mail address that you could try

Update, new link says it was a county borough (satguru).

this looks like a likely 'answer', or lead:-

Stockport isn't a county, but a suburb of Greater Manchester. It was once in Cheshire and was accorded County borough status in 1889. In 1974, they floated the idea of becoming known as Manchester South FC.
www.footballis.com/goodbyehorse/Teams/Stockport.htm

In 1890 the Club changed their name to Stockport County Association Football Club (it is believed as a result of Stockport becoming a County Borough in 1889). This name, which stirs the heart of every County supporter, has thankfully stayed with the Club ever since. This may seem a strange comment until one realises that in 1974 (after boundary changes) the Board of Directors at County very seriously considered renaming the club Manchester South F.C. It is safe to say that if they had, the club would probably not be existence today.
www.stockportmbc.gov.uk/county/history.htm