As far as I know, the Studio version is valid for 3 devices. And if you change your computer and have already installed all licences, you can deactivate the licences used on the Blackmagic page in your account. Then simply reactivate them on the new device.

Yes, it can be installed on 2 devices, and it looks like the 2 installations can even be used simultaneously. But with the third install, both previous ones expire, so be careful when changing computers and such... Another option is of course to install the free version on the "other computer". Resolve Free and Resolve Studio are not radically different; the most frequently used functions can be found in both versions anyway, but Studio has the "specialities" that I wouldn't want to do without!