Models have to be careful with this…and familiarize themselves with what they can and can’t discuss (whether in live chat, or a private message), because I got permanently banned from a texting site a few years ago. It was after I’d responded to a member (wanted info on how to talk to me outside of that particular site) by telling him to follow me on Twitter.
If the model has a Twitter account (Many cam models do, but not all do), just follow her on there where she can speak more freely about her various profiles.

She may or may not use the same model name on other sites. Guys will sometimes ask models “What are other sites are you on?,” yet when the model suggests they follow her on Twitter, they quickly respond with “I don’t have Twitter.”

Okay, um…so get on there then…smh.
If a model isn’t giving you an answer about other sites she’s on, she’s not “being rude.” She’s probably not allowed to discuss other sites…or she thinks you’re trying to get a cheaper rate on the other site…or she has other valid reasons she just prefers you interact with her on the current site (Likes the site better…more frequent payouts…more freedom…etc.).