Renee is speaking with Manuela when she says these words. In the quote, she's referencing a memory she has of spending time with Paul Nguyen. Renee describes Paul as "strikingly handsome" and "a perfect synthesis of masculine good looks and Asian gentleness." She also remembers having a conversation with him and being surprised at how he was "so utterly devoid of any form of snobbery". At the end of this conversation, Paul leaves and thanks Renee warmly. This is when she says,
I realized that in his presence I had forgotten even the very notion of trying to hide who I was.
With this thought, Renee is speaking to the connection that she had with Paul. During their conversation, she felt at ease, like she could reveal her true self without worry. This isn't something that you can do for just anyone, so it shows how much she cares about Paul.
This also shows us that Renee is in the habit of not showing her true self. That says something about her as a character. More specifically, it tells us that she isn't fully confident in who she is. There are parts of herself that she doesn't like and that she doesn't want other people to see for fear of judgment. Otherwise, she wouldn't feel the need to hide anything from anyone. This line actually adds a lot to the development of Renee's character. It tells us a lot about her internal dialogue and how she presents herself to others. It does more than just share how comfortable she felt around Paul.