The statutes governing limited liability companies are found in Chapter 4 of Title 29 of Arizona Revised Statutes. Refer to A.R.S. Sec. 29-601 and the statutory sections that follow for specific information.
Name availability can be checked at the Arizona Corporation Commission, and can be reserved on-line for a period of 120 days.
A checklist of the legal information needed to organize and prepare operating documents for a limited liability company in Arizona as well as other considerations in organizing a limited liability company can be found here.