No — bidding is not anonymous. While an item is running, the room sees who is winning, by name. When it sells, it says who won it.
If you have been outbid you are told who by. That is the format working as intended.
Why it is not anonymous
A live auction is a room. Part of what makes bidding feel real is that the other bidders are people rather than numbers — and it is what stops a show feeling like a slot machine.
A bid is a promise by somebody. An anonymous promise is worth less, and the strike that follows an unpaid win would mean nothing. Is a bid legally binding?
It makes shill bidding visible. A store bidding on its own items is far harder to hide when names are shown — and that protects the price you pay. How do I know the price is fair?
What is shown
The display name on your profile, which is yours to set. Not your username, not your phone number, not your address.
So the practical answer to "can I keep my name out of it" is: change the name. A first name, or a name you are known by, is entirely normal and nobody is checking. How to change your name
What you should not do is impersonate a real person or a business, which is a different thing and is against the rules.
What stays private either way
Your address and number — only the store you buy from, after you buy. Who can see my delivery address?
Your other purchases. Nobody sees what else you have bought.
Your maximum, if you set one. The room sees the current price, never the ceiling behind it.
The reserve, which is the seller's and is never shown to anybody.
If you would rather not be seen bidding at all
Buy at a fixed price instead of in a show. A fixed-price purchase has no room watching it. Auction versus fixed price
Leave a pre-bid where the store allows it, and do not attend. You are still named if you win, but you are not in the room while it happens.
If someone is harassing you over a bid
That is not a privacy question, it is a safety one, and it is treated as such. Report it. How to raise an issue
More: can I see who else is bidding, how to change your name, who can see my delivery address.