Thanks for using the LotusLive Notes Forum.
If you have multiple domains verified and configured, then you can certainly have email@example.com and firstname.lastname@example.org. They would be treated as two separate users, but mail could easily be forwarded from one account to the other via a user mail rule. A rule with this purpose would be configured in domain1 and contain these criteria: "WHEN all document, THEN send full copy to email@example.com"
An alternative situation would be if you have one domain but a user that needs two addresses. Let's use User1@domain1.com and SameUserDifferentName@domain1.com as examples. While we do not support aliases in a hosted environment, you could simply create a new group titled "SameUserDifferentName" and include "User1@domain1.com" in that group. Mail sent to either address would be delivered to User1@domain1.com