Yes, every document you create is automatically private. Other Overleaf users can't see your files in Overleaf unless you deliberately share the links to your documents.
For each document, Overleaf creates a unique token used only for the link to that document. It is almost impossible to guess the token, and hence the link to your document is known only to you.
Please note however that if you publish the link to your document on a website or somewhere public, anybody can use the link and the website where your link is posted might even be included in search engines.