ehow ...

http://www.ehow.com/how_4691717_register-business-name-arizona.html

the page lists several other ehow articles, in a side bar:
http://www.ehow.com/how_7548287_arizona-business-owners-name.html
http://www.ehow.com/how_6892856_do-name-pima-county_-tucson_.html
http://www.ehow.com/how_6553377_apply-register-trade-name-arizona.html
http://www.ehow.com/how_7253093_register-small-business-arizona.html

http://www.azsos.gov/Business_Services/TNT/
Search for Registered Names
Trade Name and Trademark Handbook
Trade Name Guidelines 


The Trade Name Guidelines state that a company name registered with the corporate commission does not need to also be registered with the Secretary of State, because the two offices share records.


http://www.cc.state.az.us/Default.asp
Arizona Corporate Commission

1st link

from a sponsored link on lycos (search term: how to register a company name in arizona): http://www.legalzoom.com/index1v.html.