Do I have to capitalize the word Pizza in Mike and Mary's Pizza

Yes if its part of a title.

It depends.

'Mike and Mary's Pizza' is most likely a place, and a noun is a person, place, or thing. If it is a person's name, a place (such as a street name, name of a place, a city, a country, a town ...) it must be capitalized. Just regular English rules.

Now, if the Mike and Mary HAD a pizza, you would not need to capitalize pizza considering it is the object. Here's an example of a sentence where you wouldn't need to capitalize pizza - "Mike and Mary's pizza was cheese." Now here's an example of where you would want to capitalize pizza - "I am headed to Mike and Mary's Pizza to get some food."