https://tvtropes.org/pmwiki/pmwiki.php/Main/BecomingTheMask

A trope that takes place when a spy, mole, Con Man or another character about to embark in an infiltration or deception mission takes an identity that isn't their own, but ends up liking said identity more than their own.

Adaptation commentary here, to be edited without warning or record:
Above and beyond adaptation choices made for formatting and fun, I don't translate some lines for a variety of reasons. The most common reason is that phrasing is hard and I don't feel like it's important enough to keep struggling with it. The most petty reason is that Klein's internal narration was annoying me so I skipped it. The most controversial reason is that it's homophobic, transphobic, or otherwise something I don't feel like writing but is still arguably important to the text, for instance, to Klein's character.
For situations I feel fall into the latter category, I will leave a footnote in the tag referring to this explanation.