There is no one definitive answer to this question. In general, it is generally legal to blog anonymously in the United States, provided that the blog does not infringe on any copyrights or trademarks.
However, there are a few exceptions to this rule, and it is always wise to consult with an attorney if you have any doubts about the legality of your blog activities.
Generally speaking, it is safe to blog anonymously if you are careful about who you identify yourself with and what information you share. It is also important to remember that no matter how careful you are, your blog may be exposed if it is discovered by someone who knows who you are.
Always use caution when posting personal information online, and be sure to protect yourself by using a pseudonym whenever possible.