If you're using the macOS client, you can add multiple orgniazations to the client the directly (via File > Log In To Another Team). Unfortunately, this doesn't yet work for the Windows or Linux client, but you can always connect to another organization via the web client (by going to othercompany.hipchat.com/chat).
Also of note, to be added to another organization's HipChat account you do need to use a separate email. (This is often trivial if you use something like Gmail, which allows you to append suffixes to your email).
Another alternative is to use guest access, which is great for temporary discussions around specific topics
...have mention name FirstnameLastname. Fe.: @MaartenCautreels This certainly helps to know who is being mentioned in a conversation. Imagine your colleague sends the following message...
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