You will start with 60 but you can increase the amount if you defeat more bosses, an example is if you defeat Cthulhu's eye your hamon bar will increase to 72, here is the list of the amount of hamon you will get after defeating each boss.
|If you defeat:||you will have:|
|Eye of Cthulhu||72|
|Brain Of Cthulhu||84|
|Wall Of Flesh||108|
Bosses not mentioned in the list above is why even dead people will not add any more hamon limits to the bar In addition, each Boss defeated your Hamon will have more damage.
If you want to improve the efficiency of your hamon you can try to obtain a Red Stone Of Aja which will increase your hamon limit and also increase your hamon's damage along with the regeneration of the hamon bar.