[Keeper of Dol Guldur]

If Sauron possessed the power to go into the void and fetch Morgoth from it, he would have been more powerful than Morgoth, or any of the Valar for that matter, and it would have been inevitable that the Valar would deal with him themselves if he was so mighty.

Personally, I don't think there would be any way Sauron would do anything more than use Morgoth's name. The Men of Numenor were honest and true, and probably not easily deceived. If Sauron wanted to trick Ar-Pharazon into waging war on the Valar he needed a legitimate story to tell him, and what better way to secure the success of his own diabolical plan then to use the name of Melkor, which if they looked, the historians could presumably actually find something on about how he rivalled the Valar in strength and power.

After he was defeated by Huan, Sauron fled into the east and did not show up again until thousands of years later, when he had begun ammassing forces in Mordor. He didn't return, he didn't give Morgoth the news of Beren and Luthien, and when he watched the Valar arrive in the War of Wrath, he nearly repented (but didn't), but didn't join his former master's forces and face utter destruction of his own self. Sauron was a traitor.

And then, he even had the gall to take his fallen former master's title as his own when his pride grew large enough. It's obvious he didn't intend on Morgoth's return - he was the Dark Lord from now on.

And like Hookbill mentioned back in the second post, Sauron didn't even have the same plans as Morgoth. Even when he worked for the lord of anarchy and evil, he was in charge of ordering and keeping everything neat. When he got his own fort after the sack of Minas Tirith on Tol Sirion, it wasn't the house of filth Angband was, it was an eerie isle of sorcery, with werewolves in the dungeons and stalking the fir forests around it.