If you're going to be picky, It's Bradford (Park Avenue) which was not the official title but the name of their ground was often appended to the name Bradford to distinguish that club from Bradford City. Curiously the latter is now frequently referred to as plain Bradford.
"Bradford Association Football Club was formed in 1907 and used the name of its ground, Park Avenue, to distinguish itself from Bradford City AFC and Bradford Northern RLFC.". The club now refers to itself as Bradford (Park Avenue) and use "The Avenue" frequently on its website.
On 3 May 1974 the shareholders agreed to liquidate the company with debts of £57,652. The supporters then registered the name as a company and began again in the Bradford Amateur Sunday League Division Four playing in the old kit of the former club. It does not state what the official name now is but the implication seems to be that it is Bradford (Park Avenue).
They remark in the website that around 2003 "Bradford (still the preferred title of the Club for many older supporters) established themselves in the top 10 clubs in the Premier Division of the Unibond League". The club now plays at the Horsfall Stadium just a mile from the old Park Avenue ground.