If you have a recognized disability, you can apply for a quiet room, additional time, or other appropriate accommodations for your licensing exam. Exact rules, and the process for applying, will vary by state. But every state has to make reasonable accommodations in the exam process under federal law.
Though there is little hard data, I’ve heard from multiple people who work for state licensing boards around the country that requests for disability accommodations are becoming more common in license exams for psychologists, counselors, social workers, and family therapists.
Note: The following opinion is a lightly-edited excerpt from the fourth edition of Basics of California Law for LMFTs, LPCCs, and LCSWs. Emotional Support Animal (ESA) letters are discussed in one of the book’s “Room for Debate” segments, alongside Emma Jaegle’s counterargument supporting therapists writing ESA letters. Note the update at the bottom of this post.