Did the S.C anime staffs consulted you when they used your code name translations? Or do they have the rights to keep your translation since it's the same series?

Homie, I'm a freelancer. As soon as I ship my manuscripts off to my editor, my interaction with the business end of things is over and done.

If it's a series where the LN and anime translators are the same, do they get to keep the LN names / stuff names too?

Even when the translators aren't the same, they'll often get sent the LN term sheet or at least reference the English LNs as they're working. When I started translating the Spy Classroom anime, Sentai actually sent me a copy of my own LN term sheet. That gave me a bit of a chuckle, but it was nice to know that even a different translator would have had the tools to maintain consistency with the light novels.