Can I buy a license on one computer and activate it on another?

Yes. The purchase email contains the license code, so you can buy through the BetterDisplay website or in the app and then activate the intended Mac with the purchase details.

Keep the email address used at checkout and the license code. On the destination Mac, open Settings > Pro and enter those details. If buying in the app activated the license on the purchasing Mac, deactivate that installation when it is not intended to use the license.

You can also purchase a license as a gift and provide the recipient with the activation details. The gift is a purchase for the recipient’s use. The usual personal-license terms still apply to sharing a license among users. See Getting a Pro License for activation and transfer steps and license terms for permitted use.