To start one without ties to your name is more difficult, at least in my state. You’d have to have a registered agent you trust and to file articles of incorporation. Plus get an EIN.

Even with an EIN, so as far as the federal government is concerned single member LLCs are basically sole proprietorships for tax purposes.

Unsure about the effect of recent ownership laws; almost certainly bad for privacy at some level.

Regardless of all that, financial institutions won’t grant credit to entities that don’t have their own income. Normally a history of income, and income not tied to a single member LLC. Been there done that. Yes my LLC has credit cards but at their core they are tied to the financial backing that my personal credit history provided.

It is possible you could jump through all those hoops and still gain a measure of privacy. There are vastly easier ways, imho.