Yes, in many social media platforms, a private account can tag someone on a story. However, the tagged person may have privacy settings that affect how they receive or are notified about the tag.
Typically, a private account has the ability to tag someone on a story. But keep in mind that different social media platforms might handle this feature differently, so it's important to familiarize yourself with the rules of the specific platform you're using.
In most cases, when your account is private, your story is only visible to those you've allowed to follow you. This is a privacy feature to control who has access to your content.
In most cases, no one can see your story when your account is private. This is to protect your privacy and control who has access to your content. Only the people you've specifically allowed or those within a certain group you've designated would be able to view it.