This question has actually been in answered in a full length book by Dr. Leslie Hotson, 'The First Night of Twelfth Night' (1954). Dr. Hotson argues that Twelfth Night is the 'working title' of the play, as the play was written to be performed on Twelfth Night (that is Epiphany - the twelfth day of Christmas - and a day of huge festivity in Elizabethan times) at the court of Queen Elizabeth.
It is difficult to find any evidence within the body of the play itself that explains or even hints at the reason for calling it 'Twelfth Night' otherwise. Scholars, prompted by Dr. Hotson, largely agree now that its subtitle, 'What You Will' (meaning 'Whatever you like', or 'What you wish for') was probably the title it was known by in Shakespeare's day.
'What you will' fits far better with the theme within the play of wishing for something to happen (Viola wishes for Sebastian to be alive, Malvolio for Olivia's love, Orsino for Olivia's love, Maria for Toby's love... and so on) - it also makes far more sense within the pattern of some of Shakespeare's other comedy titles: 'As You Like It', 'Much Ado About Nothing', and 'All's Well That Ends Well'.
Here’s another interesting piece of information concerning Twelfth Night: one critic, Leslie Hotson, contends the play was written by request of Queen Elizabeth for the festivities on Twelfth Night, January 6, 1601, in her palace at Whitehall on Twelfth Night, when she entertained Virginio Orsino, Duke of Bracciano, an emissary from Italy. “Twelfth Night,” of course, refers to the Feast of the Epiphany, the twelfth and culminating day of the Christmas season. By the end of the 15thC the riotous Feast of Fools, a kind of annual orgy celebrating a world turned upside down, originally associated with Epiphany, had been driven out of the church and forced to adopt less overtly blasphemous forms. In secular society, however, it continued to flourish during Shakespeare’s lifetime. Thus, in naming his play Twelfth Night, Shakespeare probably wanted to summon up images of the Epiphany as it was kept in his own time: a period of holiday abandon in which the normal rules and order of life were suspended or else deliberately inverted, in which serious issues and events mingled in a confusing way with revelry and apparent madness. The Riverside Edition of the Collected Works of Shakespeare provides a fuller account of this history.