Formerly known as the Identity and Passport Service, the inclusion of "Her Majesty's" in the new title recognises that passports are the property of the crown, bear the Royal Coat of Arms and are issued under Queen Elizabeth II's prerogative.
"This is a golden opportunity for the organisation formally to recognise in its title the integral role of The Crown which gives permission to issue passports under the Royal Prerogative," immigration minister Mark Harper said.
The new office is designed to make the service more easily recognisable to British citizens at home and abroad and also marks a watershed moment in the agency's departure from its association with the previous Labour government's controversial plans for a National Identity Service and ID card scheme.
The Identity and Passport Service was created in 2006 by a merger of the UK Passport Service and the Home Office Identity Cards programme.
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The service processes more than five million applications for passports each year.
"It is also important that our customers can easily recognise official government services online and save themselves money by avoiding companies who charge for information and services which are available free or much cheaper from Her Majesty's Passport Office," Pugh said.
The General Register Office will continue as part of the new organisation with its specific remit to administer civil registration in England and Wales, including collecting birth, death and marriage data and producing certificates.