Things to keep in mind for blocking someone in Hangouts
If you're in a one-on-one Hangout, you'll no longer be able to send or receive messages from the person.
If you're in a group Hangout, you'll receive a notification that someone you've blocked is also in the Hangout and if you choose to open the Hangout you'll be able to see the person's messages.
If you're in a one-on-one Hangout, your Hangout will be archived.
The person won't be able to join any future video calls with you.
If you use Hangouts to receive calls and voicemails for your Google Voice account, you need to block a phone number in Google Voice to prevent that person from contacting you.