Websocket connections with Postman
May 20, 2021, As of version 8.5.0 - Postman supported WebSocket APIs
This is not possible as of May 2017, because Postman only works with HTTP methods such as POST, GET, PUT, DELETE.
P/S: There is a request for this if you want to upvote: github.com/postmanlabs/postman-app-support/issues/4009
As the previous comment mentioned you can't do this in Postman. however, I found this Chrome app in the web store. It is very simple, but it's working really well with my local web socket connections.
Smart Websocket Client
Postman doesn't support it, but WebSocket King does.
It's not possible in Postman yet; But there is a new alternative for Postman, named Postwoman. it's open source and supports realtime Websocket and SSE requests.
Update
It seems they have rebranded Postwoman to Hoppscotch and have improved the Websocket support.