I entered a last name wrong, but has corrected it quite some time ago, but when I get an e-mail on smart matches, the wrong name appears even though it is correct when I look in my family tree...
When was the last time you got an email with the incorrect name? It is possible that SmartMatches were run at the time the name was still incorrect and therefore you received an email with the old name even though you had changed the name already.
It would help us greatly if you could send the email you received to support@myheritage.com and tell us the name of that shows up wrong. After receiving this information, I can have the tech team look into the matter.