Taking Names to Yourself (Turin vs. Gollum)

So, yesterday I came across a passage in "The Stairs of Cirith Ungol" that had never struck me as odd before; now it's piqued my curiosity. 

In the immediate aftermath of Smeagol's near-repentance scene, Sam spoils Gollum's last chance to turn from evil by accusing him as "sneaking". When Frodo wakes and Gollum calls himself "a sneak", Frodo advises*

Don't take names to yourself, Smeagol, said Frodo. It's unwise, whether they're true or false

This sounds very much like advice that Turin shd have been given. Not that he wd have taken it, being Turin: Always trying to escape who he is and what he's done, taking on names in an attempt (never quite successful) to put the past behind him. 

But then what are we to make of many-named characters throughout LotR, such as Gandalf and especially Aragorn? Is Aragorn the ultimate anti-Turin?

--John R.
--currrent reading: 42 YEARS IN THE WHITE HOUSE by Ike Hoover (1935)

*this advice is all the more effective, given that Frodo takes pains to address Gollum by his original name, which has had the effect of reinforcing that side of his personality