Interestingly this exact situation is covered in a draft letter Tolkien wrote dated August 1967. Tolkien notes that there is no connection merely "chance" or as suggested, a coincidence.
It is [..] idle to compare chance-similarities between names made from 'Elvish tongues' and words in exterior 'real' languages, especially if this is supposed to have any bearing on the meaning or ideas in my story. To take a frequent case: there is no linguistic connexion, and therefore no connexion in significance, between Sauron a contemporary form of an older *θaurond- derivative of an adjectival *θaurā (from a base √THAW) 'detestable', and the Greek σαύρα 'a lizard'.
The Letters of J.R.R. Tolkien, 297 Drafts for a Letter to 'Mr Rang', Aug 1967
Other etymologies for the name are given in other posthumously published works, including The Lost Road and The Silmarillion. The first, from the Lost Road suggests the root for 'foul' being it's origin.
THUS- (related to THŪ?) *thausā: Q saura foul, evil-smelling, putrid. N thaw corrupt, rotten; thû stench, as proper name Thû chief servant of Morgoth, also called Mor-thu, Q Sauro or Sauron or Súro = Thû.
The Lost Road and Other Writings, Part Three: The Etymologies
In The Silmarillion, the name is suggested to derive from the element thaur:
thaur ‘abominable, abhorrent’ in Sauron (from Thauron).
The Silmarillion, Appendix