Naming - everything bagel as a flavor

If we want to make an everything bagel flavored product, such as a specific type of nut, can we call it Everything Bagel Nut (Pear's Snacks)? Or does it have to be Everything Bagel Seasoned Nut (Great Value) or Everything Seasoned Nut (Nice)? We are flavoring it with the same spices that are used on an everything bagel. I wasn't sure if we could put bagel in the name if it wasn't a bagel or contained bagel as an ingredient. 

If you don't use bagel as an ingredients, I don't think you could use it in your product name as it might be misleading. Everything seasoned nut sounds good.

I'd do a little market research into this name.  A quick search through the app for my local grocery store shows a company selling an "Everything Bagel Hummus", another selling an "Everything Bagel Street Tortilla", an "Everything Bagel Egg White Wrap", some "Everything Bagel Seasoning Virginia Peanuts", etc.  Since "Everything Bagel" is a stand-alone seasoning available for bulk and retain purchase, I don't think it necessarily misleads a customer that a bag of nuts doesn't contain bagels.  So long as the packaging gives a reasonable presentation of what I'm buying, via a clear window in the bag or a accurate picture of the nuts covered in the Everything Bagel seasoning, I'd defend that product name to a regulator.

The FDA is less diligent and timely in establishing standards of identity, you can probably call it whatever you like as long as it isn't obviously deceptive.

In more strictly regulated regions or foods the key is likely going to be the use of "flavored" or an equivalent contextual term.

I have "Everything Bagel" seasoning in my kitchen right now. Yummy!