No, you should not buy a new license. We're receiving some inquiries on whether one should buy another license if a username is changed, for example if there is some IT re-organization, or if person simply finds another job. This subject is even touched in some independent reviews (like this one), which we see on the Internet.
Dear customers, you have the right to transfer your license for free, if your username is changed for some reasons. Just email us at firstname.lastname@example.org with your inquiry, and we'll inactivate your product license key, allowing you to activate it again with the new username. For sure, a change should be reasonable, i.e. we should see that this is a transfer of your activation to a different username, and not a transfer of license to another person.