No breed will come from that mix. An Eastern Egger is a chicken that might have some relationship to a blue or green colored egg. Their feathers can be any color or pattern, they can have any type of comb, any color of legs, be any size, and may or may not have the blue egg gene that gives you the blue or green eggs. Since that EE is a male he won't lay eggs, you won't even know if he has the blue egg gene or not.
A Black Star is not a breed, that is a marketing name for a black sex link. The mother is usually a black and white barred hen (usually a Barred Rock, Dominique, or Cuckoo Marans). The father can be one of many different breeds with different colors and patterns (Black, Red, Blue, even White in some cases).
By crossing an EE rooster of unknown genetics with a Black Star of unknown genetics you might wind up with chicks that are pretty much all one color/pattern but are much more likely to get chicks with a wide range of colors/patterns. Whatever you get they will not be a breed but a mix. I kind of like that because you never know what will hatch. That can be pretty exciting.
