Language convergence happens in entire communities over hundreds and thousands of years. It's why there are so many French-rooted words in English. It does not apply to an individual conversation
I like code switching best for the case where am individual subconsciously goes back and forth between two styles.
I also like assimilation for the actual process of an individual merging their speaking styles with that of the majority's style, which could then lead to code switching if they interact with both groups separately.
I like this better than the solved answer, but I suppose this is more narrowly applicable to when the one doing it is already a fluent/native speaker of the speech style they switch into.
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Mirroring