Haqq is a surname of Arabic origin commonly found in the Indian subcontinent but also in other parts of the Muslim world.
Al-Haqq (The Ultimate Reality) is one of the Names of God in Islam, and used in the second half of a compound name, commonly succeeding Abd or Abdul to make Abdul Haq.
Haque - A common last name in Saudi Arabia, Pakistan, India, and Bangladesh is also known as an ethnic English surname dating back all the way to the 1670s.
English Haque seemed to have originated from the Durham-Yorkshire region of the United Kingdom and it is believed to be a variant of the Hague surname which is still common in both the UK and the United States present day.
There are records of English Haques in the United States from websites such as myHeritageDNA and Ancestry.com dating back to the 1800s.