This is also happening to me in both the Outlook and the Gmail plug-ins. I don’t save all my thousands of leads as contacts and often the HubSpot panel in both platforms will show their email address instead of the name, and then their email address directly below it as in the screenshot provided by @cpktoes . I would like for the panel to show the name as it appears in HubSpot.
Another reason why is sometimes Gmail will auto-add a contact to my Contacts with Bob Smith as the name, but the email address is a shared account like finance@company.com. Then next year when I reach out, I update the name in HubSpot with the new finance person but Google has the old name (I don’t care about Google Contacts, I ddin’t want it save there in the first place). HubSpot should be my primary data source. So I want to be able to rely on HubSpot’s panel for the true name of the contact I’m reaching out to.