There is no way for the creator of a public Google doc to see via the Google Docs interface who's opened the document, even if the person opening it is signed in to a Google account at the time. See this article for more detail:

Explicitly shared [to a finite list of email addresses] documents show the name and avatar of users who have currently opened the document. It also shows a full history of edits made by each user. In contrast, publicly shared documents show placeholder animal profiles such as “Anonymous Badger,” “Anonymous Kraken” and “Anonymous Camel” to represent users who are currently viewing the document.

You can test this for yourself with two Google accounts and two web browsers (e.g. Edge and Internet Explorer). One account will create the document in the first browser, and the second account will view it in the second browser. Doing it this way keeps the two sessions separate.

In the first browser, sign into your first Google account, make a Google doc and make it public:

• Go to docs.google.com and start a blank document. Give it a title and some garbage text if you want.

• Click Share at the top right. A popup will appear giving you some options.

• Click change to anyone with the link.

• Click Copy link and then Done. Leave this window open for convenience. You will be looking at the document again in a moment.

In the second web browser go to docs.google.com and sign in to your second Google account.

• Paste your document's url into the address bar. When the document opens, you'll see a round icon left of the Share button representing the document's creator. Hovering over it will reveal the name associated with your first, creator, Google account.

• Leave that second browser window open and switch back to the first browser. You will see a different round icon left of the Share button in your document. Hovering over it will reveal a placeholder label as in the article I linked to above, not the name of your second, viewer, Google account.

If you want you can sign out of Google in your second browser, reopen the document, and see how that affects the pseudonymous placeholder you see in your first browser. It will probably change, but will still be pseudonymous.

I wrote at the top that the Google Docs interface won't reveal to a document creator anything about its viewers. But a malicious document can contain links which seem to point somewhere useful but actually go to a malicious domain which might record the ip address of viewers or try to install malware. Google Docs tries to help here: its default behaviour is that a click on a link in a document will show the url that link actually points to, and you have to click again to open the link. In Google Docs go to Tools>Preferences to check this is switched on.

tldr: creators of public google docs cannot see who views them, but viewers can see who created them. But you still need to be sure you trust links embedded in public Google docs before you click them.