First it was rumored that the LG Star will use the Optimus 2X name in its home country, only. But they might actually use it internationally where they've already used the Optimus name for a while. They could expand on that brand name, and add 2x to it to emphasize the fact that it has a dual core chip – the Tegra 2.
The LG Optimus 2X is going to be the world's first Tegra 2 phone, so I'm sure that whatever name it gets, it's going to be one extremely popular phone, especially if it comes out at least a month or two before anyone else. It's going to set the standard of performance for 2011, even if it arrives with Android 2.2 instead of Android 2.3, as long as they optimize it for dual core chips.
Here are some demo videos to see what the LG Optimus 2X can do: