Saurons Plan

[Firnantoonion]

According to Letters, by the end of the Third Age, Sauron had come to believe he was Morgoth.

Morgoth simply meens black lord (or something like that), when you only look at the meaning of the word well, Sauron did have become morgoth, just not Melkor, but an other black lord in an other time.

furthermore Tolkien states that sauron only was less evil than his master in that he served a master for a long time. after being his own master for such a long time, I don't think he would try to free Melkor, as he did when he betrayed the numenoreans. he now only wanted power and you have the most power when you're your own master.