“and is 15” in depth”

Are you sure that is right? That the hood is 15” from front to back? Your gas stove is 24-27” deep. I don’t know how a hood could only be 15” deep. Provide a brand name and model number.

What do you mean ”I received a 30” range hood”. You mean you did not buy it yourself? Why aren’t you buying your hood? Or are you talking about a cabinet surround hood? Not enough information in your post.

35" seems too high. IIRC the specifications for my hood insert stated 30"-32" above the cooking surface. What do the specs on your model recommend? Is it a telescoping model?

Thanks for your responses. The “custom” wooden cabinet hood came insert ready through a reputable supplier as directed by my kitchen planner. I paid for it. The insert is a Kobe Brillia SQBF-500-1 30” rated at 550cfm. Kobe recommends a vertical clearance of 26-30”. What I received will accommodate the insert but is indeed 15” deep, 30” wide and positioned 35.5” above range which can’t be adjusted downward. At 15” I don’t come close to the front burners. My question is to confirm my feeling that this setup won’t function properly.

"won't function properly." Well, that depends on what you want and need.

Tons of people don't even use their hoods. Some don't have any ventilation. Many install bare minimum 300-400CFM to meet code without needing makeup air. If all you do is boil water you will probably find it's adequate. If you do pro-style cooking/stir frying/cast iron steak it's probably not - but that's something that should have been discussed before appliances were chosen.

Ceiling height doesn't matter for venting. What does is the CFM, your duct size, your duct path, and whether you have makeup air (most places require MUA at 550 CFM). Most designers would recommend going 6" wider on the hood than your cooktop but it's not a requirement.

Plenty of hoods do not project in front of the stove. Mine is 19.5" deep. I would love more, especially to fully cover my high powered front burners, but my choices were limited by our builder. 15" seems very small but is probably similar to a lot of OTR microwaves.

The biggest issue I see in your set up is not meeting the hood requirements for mounting (26"-30"). It seems like you are looking to lodge a formal complaint with your designer; if that's the case, this is your best shot, as your hood is being installed outside of the manufacturer's requirements.

Thank you.