There were two reasons for this secrecy. First, the revelation would only worsen their situation, especially now that they were being targeted by forces Greg decided to align himself with. Second, making Claire's identity public would only embolden her further.
She was already acting like a tyrant under the title of "Alpha Zion's future Luna," throwing her weight around and causing trouble. If people knew who she truly was, would she try to rule over everyone like she owned the entire pack?
Still, Levi allowed her to run rampant—because this was Zion's plan. It was his decision to use Claire's identity to hide her in the pack. So if anyone deserved to bear the consequences of that choice, it was Zion. Let him be the one to deal with the chaos and discomfort. Let him suffer the consequences firsthand. In Levi's mind, this was the best way to teach Zion a much-needed lesson.
