Shes trying to hide what she is though. Every suggestion would make it clearer what she is 😂
Having her be more passive agressive or hostile in chat could be the way to go without having her out her allegiance the second you meet her.
She could just say "Travel? With you? I'm not that desperate for help" or something of that nature.
She mentioned it in one of her dialogs I had with her that she is a member of Creche K'liir, followers of Selune.
I was surprised because she does mention Vlaakith an awful lot in other dialogs.
I believe it was a camp dialog although I'm not certain.
I always speak to each companion every time I go back to camp for a rest whether or not there is a (!) over their head or not.
When she mentioned her Creche in my last playthrough, she didn't mention Selune at all - Although depending on the exact wording, it could mean they're in the Tears of Selune, the trail of rocks that follow the actual moon Selune in its orbit around the planet. Any chance of a screenshot?