Could this be My Three Tyrant Brothers?
Given a name from the days of the week. As a slave she was called Wednesday. When she was on the verge of death because of a small revolt, "finally found you." Just overnight, I was told I have three older brothers. Apparently, I am the key to undo the curse on the Askanier Imperial Family.
This review, admittedly somewhat critical, mentions the color-changing eyes, and she does have golden hair.
A story about cursed royalty with mood-ring eyeballs, focused on a girl given Tragic Abused Slave Backstory #12, labeled as 'isekai' only because the author wanted to ride the 'isekai popularity train' when it's really no more than 'sometimes I dream that I lived in another world where there were things called 'planes' and 'cars' and I had a little brother' so... I mean, it counts, but not really.
Found with a search for
manga slave "eyes change color"