Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hello Dimitry,
You do not need to purchase the software again. You need to deactivate the product on your first computer. To do so you need to login into your Microsoft Account.
You can follow the instructions in the link below :
https://support.office.com/en-us/article/deacti...
Hope this helps,