I want users within my company (not anonymous users which I understand to be anyone with a URL) to be able to see confluence pages but not create or edit pages.
If there is a way to control who can be an anonymous user that would also work.
No.
Anonymous access is the only way to use Confluence without a licence.
You can't control who can be anonymous - to control access by who someone is by definition, means you have to know who they are, so they are not anonymous any more.
Could I keep their name anonymous, but specify that they be in my company's domain?
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Yes, by obfuscating their names on their accounts. Although that will apply everywhere.
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