Absolutely not. The reason I say that is because there is not and never has been a County Derry.
County Londonderry was formed in 1613, mainly from the old County Coleraine, and remained in existence until 1972 when it ceased to be used as an administrative entity. The area is now governed, since 2015, under three different districts; Derry and Strabane, Causeway Coast and Glens and Mid-Ulster.
The shiring of Ulster was undertaken in 1585, when the area was described as the County of Coleraine. Following the defeat of the Irish earls and the confiscation of their lands in 1609, English colonization was undertaken by livery companies of the City of London and the Honourable Irish Society (founded 1610). A charter of 1613 established the county of Londonderry, which comprised the old county, O’Neill lands of Loughinsholin, and small parts of Donegal and Antrim.
Despite not being used by government as an administrative area both County Londonderry and the province in which it is contained, Ulster, are still used by sporting and other bodies and of course in genealogy.
County Londonderry is one of the six counties that form the present day Northern Ireland which became a separate jurisdiction from Ireland after 1922. It is also one of the 9 counties of the Province of Ulster.
The use of Derry is absolutely correct for the City but not for the County. In deference to Northern Ireland however the City these days is called Derry/Londonderry