You certainly may write the book and include the name of the person who hit you. But if you intend to distribute the book to others (even if you give it away for free) you do run a risk that the DUI driver will sue you for defamation. If everything you state in the book are either true facts that can be verified or are clearly your opinion then the DUI driver would lose the defamation suit. But you'd still incur the cost of defending that claim, and that can get costly. At a minimum, as others suggested, I'd have a lawyer familiar with defamation law read the book and advise you of any parts in it that may expose you to liability for defamation. That still won't prevent you from getting sued.
Even leaving the person's name out of the book doesn't entirely solve the problem for you. If the facts given in the book would make it possible for others to identify the DUI driver you might still face a defamation claim.