Yes, you may need to. Google sometimes needs you to verify you want both versions. Dumb I know, but that’s Google for you. Typically, once you’ve verified one version, Google can easily verify the other using the original verification method (wait a week or so to see).
Once you’ve set your preferred domain, you may want to use a 301 redirect to redirect traffic from your non-preferred domain, so that other search engines and visitors know which version you prefer. Once done best practice is to leave all verified versions in Google Search Console.
Now you can verify the whole domain using Google search console.
Check back to the actions in week 1 to see how to do this.