I have encountered the author of Tehillim referred to directly as David HaMelekh. However, on no small number of occasions, I've also encountered the author of Tehillim referred to as "The Psalmist" (presumably "HaMezamer" in Hebrew).
For those who hold that David HaMelekh indeed authored Tehillim, why refer to him as "The Psalmist"? On a somewhat related note, why are verses in the prophets sometimes referenced by saying "The prophet (HaNavi) said ..." Why not simply refer to these authors by their names?