This is from the National Archives website:
"A person can legally change both their forename and surname without any formal record of that name change being recorded. Documented name changes, by statutory declaration before a Commissioner for Oaths or by deed poll sworn in front of a solicitor or magistrate, are private transactions and no permanent record is kept. Only if a deed poll is enrolled in the High Court and advertised in the London Gazette is there a permanent record.
Enrolments of deed polls are found on the Chancery Close Rolls in C 54 from 1851 to 1902, or in the Enrolment Books of the Supreme Court in J 18 from 1903 onwards. The nominal indexes to C 54 refer to the individualīs former name, whereas those for J 18 give both former and new name. All deed polls have been advertised in the London Gazette since 1914, to which there are quarterly indexes. Enrolments made within the last five years are still held by the Royal Courts of Justice.
Change of name could be undertaken by Royal Licence from the 17th century, and a record of it often appeared in the London Gazette. Changes of name by licence were usually done by beneficiaries under a will or as a party to a marriage settlement where a man might be required to take on the name as a requirement of the inheritance and contract. Enrolments of Royal Licences are held by the College of Arms, but the warrants are held in The National Archives. Warrants before 1782 are in SP 44, from 1782 to 1868 they are in HO 38, and from 1868 onwards in HO 142.
Some changes of name were made by private act of Parliament, which was uncommon and also more expensive. Private acts of Parliament are held in the House of Lords Record Office,
http://www.parliament.the-stationery-office.co.uk/pa/genlinfo.htm.
See W P W Phillimore and E A Fry An Index to Changes of Name Under Authority of Act of Parliament or Royal Licence and Including Irregular Changes from 1 George III to 64 Victoria, 1760-1901 (London, 1905).
Foreign Nationals Change of Name
Restrictions on change of name were placed on enemy aliens from 1916 and on all foreign nationals from 1919. The only exceptions were when a new name was assumed by Royal Licence, or by special permission of the Home Secretary, or when a woman took her husbandīs name on marriage. The restrictions were finally lifted in 1971."