Your reputation can enter rooms before you, but character decides whether it stays welcome.

Reputation opens doors and cannot hold them. Whatever people have heard gets you an initial position, and then everything after that is decided by what you actually are: whether you follow through, how you behave when it is difficult, whether the account matches the person. The second part is the durable one.

Rather than working on how you are perceived, work on what would still be true if nobody had said anything about you in advance. That is what determines whether the welcome lasts. It is also the only part you fully control.