No, not if you don't want to. Worth noting there's two elements here. You have a model that must be setup in the Nest app, but it will appear in the Google Home app as well if you login with the same account. This assumes you login with a Google account, and are not using a legacy Nest account. If you're using a Nest account still, you'd need to migrate to a Google account to get that functionality, but it's not mandatory.
FAQs about accounts for the Nest app - Google Nest Help
