More info for home inspectors becoming FHA approved can be found on Mortgagee Letter 04-29. The roster of FHA inspectors can be found here https://entp.hud.gov/idapp/html/insplook.cfm ,
I do recommend and refer both 1 lender and 1 home inspector, who guarantees his work (and he is licensed and bonded) because I have referred them to 20+ clients now, and all have been satisfied. That is exactly how I explain it to clients, that they are free to use anyone they want and I am fine with it, but I have 20+ referrals this ABC and never had a problem.
Even though we are sincerely only trying to help, it could come back on us if we urge them to only use one (fill in the blank, any referral) when it is their choice to choose.
Best of luck.