A city only has one name, therefore it's name is a singular object. So when you include it in an address, the name is a single "part" of the larger collection.
This is a very good question. In general, you can help yourself work through any confusion by trying to express the idea more precisely or in a slightly different way. I'll use each of your examples to explain this a bit further.
EX1: All lizards have a head width, but that isn't what you measured. You measured the different head widths of a group of lizards, or "the head widths of some lizards." I would at least add the "some", but perhaps it would be better to include the actual number.
EX2: You are talking about the growth rate of all birds, not, say, the growth rates of different species of birds.
EX3: Each of two populations has a mean height, therefore there are two mean heights. You are saying that the mean heights of these two populations are different.
EX4: Dogs have noses is correct, but this is a bit inconsistent. For example, dogs have a sixth sense that lets them know when someone is coming, and they have a nose for trouble. People have minds, but they have a combative streak. So, when you are talking about a shared characteristic of all dogs, you use the singular, but when you are talking about something that each dog has, you use the plural.
Best Answer
Perhaps a little rephrasing is in order:
This is a little clearer to me. If you wanted to leave the sentence as it is, you're referring to two codes: "Make sure these codes match", so you'd use codes and match. In mine, you're referring to one code at a time, "Make sure this code matches that code", so you'd use code and matches.