Learn English – When can you respond with “affirmative”

In some cases, height is countable:

[uncountable, countable] the measurement of how tall a person or thing is

In this sense, height means measurement, and measurements are countable. Your sentence with "...various heights" is correct.

Height is uncountable when it refers to the property of tallness:

The height of the mountain did not discourage them.

The mountain has some uncountable amount of height.

Even if we deal with multiple mountains, we can still have a single uncountable height property:

The height of the mountains did not discourage them.

This means the tallness of multiple mountains did not discourage them. It's similar to, "The fact that the mountains were tall did not discourage them." (But this is very awkward phrasing.)

The heights of the mountains did not discourage them.

This means that they measured (or otherwise learned) the individuals heights of multiple mountains (e.g., one was 5000 feet, another was 6000 meters, etc.) and were not discouraged by the sizes of the measurements.

(Note that the plural heights (and rarely in the singular) has yet another possible meaning of "high places," as in, "I have a fear of heights." That is not my intended meaning of "heights" in the above sentence.)

For s similar uncountable property, consider speed:

We need more speed to outrun our opponents.

And, by comparison, consider the countable form of speed:

The runner's speed was 6 kilometers per hour.

The runners all ran at different speeds: 5 kilometers per hour, 6 kilometers per hour, and 7 kilometers per hour.

There are as many answers to this as there are situations.

In informal settings, one might only give their first name. So, if I'm at a bar and I start chatting with someone, I would usually only give my first name... or if I'm being introduced to new people by friends, I'll only give my first name.

In formal or business settings, one might give both first and last name. So, if I'm introducing myself to a business partner, I'm more likely to use both first and last names. This is often because you want people to be aware of your full name, so if they need to find you later, they can do so.

When giving your name because it may appear on a list, as when checking in to a hotel, it's common to give your last name, as that is usually what the reservation is filed under. So, as an example:

Receptionist: Welcome to the Hotel. May I have the name on the reservation?
Guest: It's under Bond. James Bond.

This could be the case in many different situations other than simply at hotels.

Since you ask what the significance of last names is... well, there are many groups that only use surnames as means of address... particularly within the military or on sports teams. Often, only the surname of the person is known in those cases, with the possible addition of a first initial if the surname is common.

James Bond is a member of a military organization, and started out in the British Navy, so it makes sense that he would introduce himself emphasizing his last name.

Also note that the original Bond books were written in the 1950s and the movies first came out in the 1960s both of which are eras that are much more formal than modern times, so much of the characterization of James Bond stems from that time.