I am looking for the most common way how people in US/Canada spell something like this, preferably in accordance with Chicago Manual of Style. What is the right way to spell the title "Diana and Tom's Grill" or "Diana's and Tom's Grill"?
"Diana and Tom's Grill" is very preferable. This is because "Diana and Tom" act as a collective noun, such as "water" and "grain". But I point out that "Diana and Tom's Grill" is a proper name. As such, one could in fact use a second possessive with "Diana" and just claim it's the chosen name of the place. In English, when dealing with proper names, anything goes. But stylistically, English-speaking people would look at the two possessives in the name and conclude that the author was not a knowledgable speaker of English due to their failure to identify the collective noun nature of the premise in question (i.e., the grill).
Hope this helps!