@TonySchmidt I am not sure I am following you. Please clarify and supply screenshots.
If my inbox is connected and a new contact sends an email, then only their email is known not their name. If the email already exists then the contact name is what was last saved. If you change the name in HubSpot then it is likely to change the name for all activities for that contact record.
example - finance@company.com sends an email
if the emails exist as part of contact Bob Smith then it is shown as Bob Smith regardless that is Susie Jones. You can update the contact and change the name to Susie Jones.
If your inbox is connected then you are likely to have new contacts automatically added as emails are sent to you.