In Arizona it seems as if almost anyone will trim your palm trees.  Before going with the guy who shows up with no company name or small landscape business, consider the risks.  Although many are willing to do the work, they may not be properly equipped or properly insured for the work.  Landscaping insurance typically only covers workers up to 10 feet, so if they go past that their insurance is void and it puts the homeowner at risk.  In addition, there are many palms that are not native to Arizona and require special care to ensure their health.  Call someone with the proper insurance, equipment, and experience.  Call Heartwood Tree Care.