Change of Culture, Names and Status.
In Jerusalem they were from noble and royal families.
In Babylon they were taken as slaves who will serve in the kings palace.
Their names were in relation to their believe in the one triune God. So in Babylon they changed their names to that of their idol gods belonging to the land in order for them to convert them from their faithin God.
It was not their choice to be eunuchs, They were forced by the change that they were experiencing.
No they did not make any compromises but they stood firm in their believe in God although they were ready to serve in the kings palace.