You can create email aliases for yourself, an organization, or an event (such as 'firstname.lastname@example.org') through the email alias creator. An email alias is personal to you and delivers mail into your mailbox, like your official email address does.
Note: When creating an alias for a department or organization it is strongly recommended the creation of a Google Group. This allows email to be received by more than one person and is easily updated as group members arrive and leave. A personal alias is permanently tied to your email address and can not be changed.