Are there any guidelines for labeling axes in plots/graphs when the "unit" is "number of people"?
You always have to distinguish between the quantity and the unit. 

All the quantities referring to a number of entities have unit 1, so you don't need to put any unit after the number.

About how to call such kind of quantities, you're actually relatively free to decide, depending on the specifics of the case at hand. You can certainly call a quantity that counts certain elementary entities X as number of X. But, in case, don't use amount of X because that has a specific meaning in chemistry.

Examples of quantities called number of X can be found e.g. in the IUPAC Green book: 


  N is the number of identical (periodic) events during the time t. (p. 13)
  bi gives the number of electrons which occupy a given orbital energy level εi (p. 19)


Even better, if that number is a recurring quantity in your paper, label it with a symbol and use that symbol to label the axes: "Let nr be the number of people who always wear red trousers [...]".