
Check couple of things:
- Make sure database name's are different or
- not already exist on the SQL server
- make sure SQL server versions are same.
BTW, I highly recommend in your mentioned scenario simply move the Content rather performing a restore:
- Install and configure new farm on new domain
- Create and configure the Web application, Service Application etc.
- Now backup and restore the Content DBs to new sql server and mount to SharePoint.
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