There are various terms for this.

One is "Zelig syndrome" after the protagonist of the eponymous Woody Allen movie from 1983

Another is "Environmental dependency syndrome" which I personally find as improper as the term "masking" as both insinuate intention and propensity of deceit.

A third one is "Chameleon syndrome" which I find best as it conveys the unintentional and semi-automatic dynamic of that "behaviour".

Personally I find it difficult to distinguish this mimicking from empathy. Or put differently: When one comes to accept this mimicking as a talent, one can, via introspection, achieve a deep insight into other people's state of psychê, which can be helpful in all sorts of councelling, therapeutic help, and conflict resolution.