Short answer
HubSpot's KB: visitors aren't added as contacts just by starting a chat; they stay tied to an anonymous cookie until you get an email address. Enter the email in the inbox's right panel to match an existing contact or create one. Messenger guests show as unknown visitors.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Ask for the email early in the chat.
3. Related
Inbox views and bots.