Perhaps a more magnanimous name than just Empire. If we do indeed merge with the Imperial Remnant this is a great idea. What about specific names. The Empire is a little too generic. There have been a ton of Empires. Ours needs to be unique, but not so it only attracts Sith, like you said. What about naming it by a geographical point of origin? (Like with Carthaginian Empire, the Roman Empire, etc.) Horuset Empire would make sense, since Korriban is really one of the birthplaces of the Sith. Or the Dromund Empire.
In my opinion, we should be building a new legacy, not simply having yet another knockoff of some variation of Sith Empire (Sadow's, Nadd's, Kun's, Revan's). We should also get a new symbol. The six arrows of Chaos are cool, but over done. I suggest a complete remodeling.
Also, a restructuring of rank commands. The reason why we have so many Sith is that Sith are given free reign and basically rule the Empire. If we were to reign it in and have the Sith as a sort of government sanctioned cult, that would probably be better. It would also put an end to the half-hazard killing of our own assets that is so common among Sith. With the new direction Ashin wants to take the Empire it would make sense to have some kind of crime and punishment laws in place, where Sith have a smidgen of immunity to the law, but can be held accountable for serious offenses.
Sith are evil. But we can't expect every underling and trooper in the Empire to be evil as well. They have to have something to fight for besides "If you don't we'll kill you." They have to believe what they are doing is right. Because, believe it or not Sith, normal people have to think that they are working toward a noble goal. If you're like "We kill people for the lulz, including you, peasant." you are not going to get a whole lot of followers.
A restructuring of command, with a few members of the Sith in positions of power, but not the Order as a whole would work toward that goal. Of course, the Order would still be given preferential treatment. Duh.