"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!