Social duplication.

Social duplication is when you talk to someone frequently enough that you start using the same terms and mannerisms as them. Usually spotted in close friends and intimate relationships, both or either of the parties in frequent contact take words and phrases, among other forms of communication and apply it in their conversations. Often, this can have a chain effect, having the people that they talk to also display the passed on mannerisms.

Person 1: Hey, Phill's been talking to John a lot lately and he's starting to talk a lot like him.

Person 2: Must be social duplication.