Yes; You have a right to blog anonymously?
Yes. The Supreme Court has repeatedly upheld the First Amendment right to speak anonymously: “author is generally free to decide whether or not to disclose his or her true identity.
The decision in favor of anonymity may be motivated by fear of economic or official retaliation, by concern about social ostracism, or merely by a desire to preserve as much of one’s privacy as possible.
Whatever the motivation may be…the interest in having anonymous works enter the marketplace of ideas unquestionably outweighs any public interest in requiring disclosure as a condition of entry.
Accordingly, an author’s decision to remain anonymous, like other decisions concerning omissions or additions to the content of a publication, is an aspect of the freedom of speech protected by the First Amendment.” (McIntyre v. Ohio Elections Comm)