The personal name is used as the organization name because at the time of accepting an invite, the user accepting the invite was not registered to any organization, as such, a temporary/standalone team is created in the backend to complete the workflow, and the user's name is used as the organization.
The first invitation to a user of a specific email domain adds everyone with that same email domain as a user under the organization to the original invitee assigned. This is the way it has always worked. The first external participant to accept the invitation to a Project becomes the admin for that external organization, and everyone with the same email suffix as that first user is added under that user's organization.
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