I can't upgrade my Mac from macOS Sierra to macOS Mojave. Admin password required
Your Mac is asking for an administrator name and password for a reason. It wants to make sure that only an authorised user is making a major change to the computer as upgrading the operating system software.

You generally cannot work around it. You'll need an administrator username and password to be able to upgrade macOS. You should consider getting in touch with the person/team responsible for this and seek their assistance.