People in the Renaissance did not refer to Titian hair.
Which is logical, since English-speaking-people in the Renaissance would only have seen Titian’s paintings of Venetian women if they had been to Venice - where they would also have seen so many women with that hair colour that it would logically be associated with the place, not the painter. Only after a century or more of the Grand Tour had filled the stately homes and art galleries of England with Italian Renaissance paintings would it have been possible to refer to ‘titian hair’ and be confident that any cultured English person would know what that looked like.
‘Titian’ became popular, at least in part, because historically red hair had been much disliked in England and to describe a woman as ‘red-haired’ was potentially derogatory; so a term that associated it firmly with culture and beautiful paintings was useful. These quotes from the OED bear this out:
1904 Dundee Advertiser 27 June 8/1 Twenty years ago hair with a reddish tinge was called ‘carrots’; now ‘Titian-coloured’ locks are reckoned a definite beauty. 1904 BENSON Challoners v, The girl..had Titian hair in golden glorious profusion. 1923 Times 3 May 14/6 (Advt.), Tecla pearls..are equally becoming whether worn by blondes, brunettes or Titians.