And by that I mean: a situation where an individual can conduct their general business activities privately within a proprietorship under a fictitious "pseudonym" or via proxy? Though I'd imagine if so there would at least be provisions within the law that would allow for one's identity to be revealed by subpoena or some other means in cases that constitute personal legal liability—especially under criminal investigations.
If I understood you right, you want to use a company name rather than your own.
Normally, that is done with a dba, or doing business as. Check this site: https://www.fundera.com/blog/what-is-dba
When your business is a sole proprietorship, meaning its not a legally registered corporation, you file for a DBA.
Registered Corporations pick a name while registering and don't have to have a DBA, but can if they want.