Changing email addresses is a self-service feature for users with an active subscription. On either the domain search or API key dashboard, click the "change email address" button, enter the new address then follow the instructions sent via email.
It is strongly recommended that if you work within an organisation, you change the email address to a shared mailbox and manage the members within there internally. This ensures you won't lose access to your account or have to manually log tickets when colleagues change roles or move on.