Is there an alternative to the word "coincidence" to describe when two say the same word spontaneously?

Is there a word to describe a scenario where two people having a conversation utter the same word/phrase together, simultaneously, and unconsciously? Something else than just a coincidence.

A jinx.

A common slang term used when two people say the same thing at the same time, said as a game among children.

A phrase often used for saying or thinking the same thing as someone else is "great minds think alike", which is like the German phrase @user3448 pointed out in a comment.

Great minds think alike has a history back to at least the 17th century:

Dabridgcourt Belchier wrote this in Hans Beer-Pot, 1618:
Though he made that verse, Those words were made before. Good wits doe jumpe.
That citation uses 'jump' with a meaning long since abandoned in everyday speech, that is 'agree with; completely coincide'.

In my experience as an American English speaker, it's often acceptable in places, such as with professional colleagues, where calling "Jinx!" might come across as childish or inappropriate.

A certain stripe of person will refer to this as a hivemind moment. Others would call it a synchronicity, though I'm a little dubious that the event calls for that word's vaguely mystical implications, and might prefer synchronism.

You could say the two people said [the same word] in stereo. Or one of the speakers could just say Stereo! as noted here from Urban Dictionary:

When two people say the same word or phrase simultaneously during a conversation (usually by coincidence), the word "stereo" would then be uttered immediately by one or both parties to acknowledge this phenomenon.

Of course, if both parties say stereo in stereo, then one would have to say Jinx!

What one says is "snap" — based on the card game of the same name. (British/Australian English — cf. "jinx" in US English.)