I think she is probably
Jupiter's moon Europa.
I have explanations for almost but not quite all the lines.
A noble daughter with the blood of ancient royalty
As Wikipedia saith: "In Greek mythology Europa was the mother of King Minos of Crete, a woman with Phoenician origin of high lineage".
Her face pale as a corpse, and heavy with lines
The surface of Europa is ice; it's mostly light in colour but is criss-crossed by striking lines called "lineae".
Her skin smooth and cool to the touch.
Europa is one of the smoothest objects in the solar system. Its surface is made of ice.
In one way, she is old and dead,
In another, she is young and alive as well.
Like any other body in the solar system, Europa is basically a big lump of (non-living) rock. But its surface is much younger, probably because of tectonic activity. OP's comment: And if the mythological Europa had truly existed, she would have died millennia ago.
In perfect step, she dances with her lover
Europa is tidally locked to Jupiter. (And in Greek mythology Jupiter (=Zeus) and Europa were indeed lovers.)
A leader who glares with angry eyes
Not sure exactly what that's about, though of course Jupiter was the leader of the gods. (The "angry eyes" might be a reference to the Great Red Spot?) OP's comment: Yes, the eyes refer to the Red Spot.
They say that he took her from her home
To become his bride, forever bound to him
Perhaps Europa was captured by Jupiter rather than e.g. being formed by impact. I haven't yet found that out. (Also, in Greek mythology Europa was abducted by Zeus. She wasn't exactly "forever bound to him", though.) OP's comment: Zeus/Jupiter abducted her as a strong bull. The moon is bound in Jupiter's strong gravitational pull. Please excuse the lame wordplay.
After all this time, she must be dizzy.
As a result of constantly rotating around Jupiter while spinning on its axis for billions of years. (And Europa's orbital period is only 3.5 days!)
The ice queen knows she cannot be his favorite
I guess this just means that Europa is not the largest or closest of Jupiter's moons.
Yet despite his many other paramours
Jupiter has many other moons.
She is loyal, never turning away her face
Again: tidally locked.
Always staying bright and brilliant
Europa's albedo is very high.
Though to you, she may seem cold and distant.
It's a long way from earth. OP's comment: Also, Europa's mean distance from Jupiter's "surface" is over 600000 km. For reference, Earth's radius is 6371 km.
Surely you know her name, or something similar
Her legacy a one-word mark for many people
Is this just a reference to Europe? (Many people are European.) OP's comment: In older atlases, the label for Evropa/Europe was typically written in larger letters than other labels.
Maybe you have seen her, but I doubt you have met
No human has been there yet.
Below the surface, she is much like you and me
It is thought that beneath the ice is a salt-water ocean. Humans are mostly salt water. Or, perhaps, "you and me" might stand instead for our planet. Europa probably, like the earth, has an iron core surrounded by a lot of rock and a salt-water ocean.
Perhaps someday, we will greet her.
I take it the author of the riddle hasn't read Arthur C Clarke's "2001" :-). OP's comment: That's quite the monolithic assumption.