Hey there @Martin18136 - so sorry to hear this is happening!

Are you using Calendar Invitations, or Email Confirmations? My guess would be calendar invites, in this case? 

For some context, with Calendly, there are two types of invitee booking notifications: Email Confirmations & Calendar invitations.

1. With Email Confirmations, Calendly sends the invitee an email notification from notifications@calendly.com and has a reply-to address that's associated with your Calendly login email. You can modify this on Account Settings page.
2. With Calendar Invitations, your connected calendar sends the invitee a notification of the booked meeting which has a reply-to address that's associated with your Add to calendar email on your Calendar Connection page.

Note: Calendar invitations are not compatible with iCloud Calendar or the Outlook Plugin (for Windows users). Users with either of these calendar connections set up as their "add-to calendar" on their Calendar Connection page will be defaulted to Email Confirmations. 

If you are using Calendar Invitations - head to your calendar synch page > disconnect your calendar by clicking the “trashcan” icon > reconnect your calendar > book a test event with yourself to see if it pushes to your calendar/the fake invitee calendar for the email you use to book the test. If this works, great! 

If this does not work, please reach out to our support team by logging into your account and clicking “chat with us” in the bottom, right-hand corner. Our support team is available 24/7 and can dig into this deeper to help you resolve it.

Thanks, and have a great day! =)