My brand new iMac is receiving iMessages sent to somebody else, how to fix this? My brand new iMac is receiving iMessages from my daughters phone, not mine. Do you have any tips how to correct this?
I have tried to restart and shut hers off on her phone.
In messages on your Mac, check that you are signed in to the account that is yours.

If not - sign out and back in to the correct Apple ID for you and not the one your daughter uses.

Assuming you are on your account - make sure your daughter's phone number or email aren't added under the "You can be reached for messages at:" section. 

This happens commonly when your Apple ID is signed in to someone else's iPhone to get apps from your account and you don't correct the messages settings. Entering your password on that phone ties their number (or possibly) email to your AppleID account for iMessage.

Going to that device and signing out of iMessage is the best way to remove that number permanently from your account. When that's done, also be sure her iPhone isn't using your Apple ID in iCloud settings - handoff could send messages from the phone directly to your Mac as well without it showing up in your AppleID account.