Do we have a psychological need to talk to people? Do we have a psychological need to talk to people?

I don't believe it's in Maslow's hierarchy, but surely.
It’s worth remembering that Maslow proffered a THEORY with very little experimental evidence to support it. Since then lots of experimental research has been done with a number of primary needs being identified. Primary needs are often those that take place implicitly and/or evoke visceral responses (typically via the amygdala) when threatened or rewarded (there’s more to it than that but just a starter for 10).

A neat summary of those primary needs can be found in David Rock’s Your Brain at Work (2009). The need I believe you’re referring to is RELATEDNESS. Neuroscientific research in this area has found that being excluded from say a conversation or group hurts us more than physical pain. Also have a look at:

The neural bases of feeling understood and not understood 
Sylvia A. Morelli,  Jared B. Torre, Naomi I. Eisenberger

Naomi Eisenberger in addition has lots more great research in this area - too much to list here

Hope this helps!