I ran into this problem recently, and had to spend a little time researching the correct answer, so I figured I would write up a quick article to show exactly how to change the license key in Office 2013.
- Open up an elevated command prompt window.
- Browse to C:\Program Files\Microsoft Office\Office15 (If you are running the 32 bit version, use Program Files (x86)
- Run: cscript OSPP.VBS /inpkey:<yourlicensekey>