When macOS starts, you are asked to enter a name and account. I wonder if this potentially personal data third-party macOS apps can read, especially the user's name or username.
I'm on macOS Big Sur 11.1.
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Yes, third party macOS apps can trivially access both your user name and full name.
A work around to this specific problem might be to create a new user and run the application as that user. However, as mentioned in another answer, developers have more nefarious ways to identify you.
Yes, you can third-party macOS apps that you install on your computer can in general read personally identifiable information.
You can add various permissions schemes, sandboxes, etc. in order to limit what information the app can access. However for a typical home user computer, it is really hard to block access to all PII while still having the app work. For example just knowing your external IP address is a piece of PII - apps that communicate with the outside world, and they're many, generally will be able to learn this bit of information.