We get error "Registration Name mismatch!" when I activate ElecKey license on the new machine.

To reactivate ElecKey, you must enter the same registration name and organization that you originally used to activate the license.
The registration info is also served as credentials, so nobody can easily use your Activation Key to activate your ElecKey license. It's important because your ElecKey license can generate license keys to unlock your protected software. From our records, you must enter the following in the ElecKey product registration and activation dialog box.