Doyle or Conan Doyle ?
From The Arthur Conan Doyle Encyclopedia
The quick answer is "Conan Doyle".
Arthur changed unofficially his name from "Doyle" to "Conan Doyle" very early in his life. As explained by his own daughter, Dame Jean Conan Doyle in the following letter to Roger Johnson published in "The Sherlock Holmes Journal" (Summer 1983) :
- 27 May 1982
- From a very early age (I don't know the exact moment, but in childhood) my father used 'Conan Doyle' as his surname. He told me that he was A. C. I. Conan Doyle - Arthur Charles Ignatius. The latter was, I believe, one of his baptismal names; he dropped it when he was no longer a Roman Catholic.
- He took the name as part of his surname because he wanted to perpetuate the family name of his grandmother and a favourite uncle. As you say in your article, one is entitled to give oneself any name without an official announcement. Unfortunately a number of officials, especially in rural areas, were not aware of this fact and when registering an event were apt to be flummoxed by a double-barrelled surname that was not hyphenated, especially when the individual concerned elicited the information that his father's surname was just Doyle! In these circumstances neither of my parents ever made a fuss when - through ignorance - they were incorrectly addressed or their name entered as Doyle. At the same time, the lapse did not go uncommented upon within the family! My father was far too big a man to be concerned over petty errors or to spend time pointing out that 'Conan Doyle' really had become his surname, and was that of all his children. Both my mother and my father's first wife considered their correct surname to be Conan Doyle, although they were sometimes incorrectly addressed as 'Lady Doyle'.
- As you know, a Knight or Dame only uses one first name, i.e. Sir Arthur, with their surname — Conan Doyle. It was always 'Sir Arthur' or 'Sir Arthur Conan Doyle', never 'Sir Arthur Conan' or 'Sir Arthur Doyle'. When it came to my brothers and myself growing up officialdom was much more familiar with compound names, so sometimes I find myself under the 'C's and only sometimes under the 'D's. I can never be bothered to correct the latter, but it doesn't mean I accept it as correct.
- What a long letter about a name! Perhaps I should just have said that my mementoes of my father's early life all bear the name A. Conan Doyle rather than A. C. Doyle.
- Jean Conan Doyle
On Arthur Conan Doyle's birth certificate, his first names were "Arthur" and "Conan" and his surname was "Doyle", so he was born "Doyle" as his father (Charles Altamont Doyle) and his grand father (John Doyle). Same for his baptism certificate from St. Mary's Cathedral: first names were "Arthur Charles Ignatius Conan", surname was "Doyle".
But as soon as 8-years old, Arthur started signing some letters to his mother with "A. Conan Doyle" . He wanted to perpetuate "Conan", the surname of his grandmother (Marianne Conan) and his great-uncle and godfather (Michael Edward Conan).
Around the age of 12, he wrote to his mother from Stonyhurst school: « I sent him [Michael Conan] a playbill and I slily changed the A. Doyle on the bill into A. C. Doyle to gratify him. » 
At this age, he was torn between his birth name and his chosen name. In a manuscript of one of his first poems The Passage of the Red Sea (14 november 1873 ) Arthur signed it "A. C. Doyle". In july 1875, he was undergratuated of the Royal London University as "Arthur Conan Doyle" but he signed 2 letters as "Arthur Doyle" to announce it to his mother. So the change was not totally done.  In june 1878 (aged 19), he wrote to his sisters Connie and Lottie signing Arthur C. D. 
The definitive change happened when he started his medical career. In june 1882 (aged 23), Arthur set up as a general practitioner in Southsea, Portsmouth. He installed a plate with "Dr. Conan Doyle, Physician & Surgeon".
His first signed article Gelseminum as a Poison (20 september 1879) was signed "A. C. D.". The second one After Cormorants with a Camera (21 october 1881) was signed "A. Conan Doyle, M.B., C.M." As well as the next ones, Notes on a Case of Leucocythaemia (25 march 1882), Life and Death in the Blood (march 1883), etc. See All articles
His first signed short story The Gully of Bluemansdyke (december 1881) was signed A. C. D. But the second one, in april 1882, Bones, the April Fool of Harvey's Sluice was signed "A. Conan Doyle, M. B." As well as the next ones, Our Derby Sweepstakes (may 1882), My Friend the Murderer (december 1882), etc. See All fictions
All publications will be signed "A. Conan Doyle" afterward.
Conan Doyle exclusively signed his letters "A. Conan Doyle" until 1903 and a mix of "A. Conan Doyle" and "Arthur Conan Doyle" after 1903. On very rare occasions he shortened to "A.", "A. C. D.", "A. C. Doyle" (only once known so far).
Example of early letters : The Remote Effects of Gout, 29 november 1884; Letter about John Barrington Cowles and The Blood-Stone Tragedy, ca. 1885; Carlyle: His Character and Philosophy, 29 january 1886; etc.
In the press
The press used "Dr. Conan Doyle" as soon as 1882 when he started as a Doctor, not yet known for his writings. The first article about Conan Doyle : Accident in Elm Grove (2 november 1882) mentioned him as "Dr. Conan Doyle, of Bush Villas." In december 1882, a report of the Portsmouth Literary and Scientific Society meeting listed "Canon Doyle" (sic) among the attendees.
Almost all articles used "A. Conan Doyle", "Dr. Conan Doyle", "Mr. Conan Doyle" or only "Conan Doyle". However, some newspapers, mostly American, sometimes used "Doyle" for punchlines ("Doyle Fights on to Aid Edalji", "Doyle not to be Referee", "Doyle to Seek Parliament").
Wife and children
See their graves or obituary headlines below:
Louisa Conan Doyle (1st wife)
Jean Conan Doyle (2nd wife)
Mary Conan Doyle (1st child)
Kingsley Conan Doyle (2nd child)
Denis Conan Doyle (3rd child)
Adrian Conan Doyle (4th child)
Lena Jean Conan Doyle (5th child)
- Letter to his mother dated 13 october 1867 (A life in Letters, p. 20).
- Undated letter to his mother, circa 1871 (A life in Letters, p. 39).
- Letters to his mother, july 1875 (A life in Letters, p. 73).
- Letter, London, June 1878 (A life in Letters, p. 107).