example:
chauntees = 34 = 30 and 4. Word for 30 is tees and word for 4 is char - combined to form chaun-tees.
chhuttees = 36 = 30 and 6. Word for 30 is tees and word for 6 is chey - combined to form chhut-tees.
So on for all the words from 20 till 99. The combination rules might not be obvious here in transcription, but they come naturally to a Hindi speaker. So in reality there are dedicated words for 1 thru 19, and then the rest are compounds formed from the words corresponding to each digit.
So, it's not like each number has a different name.
However, it's almost like that.
Basically, the numbers can be broken down into a logical tens and ones place -- e.g. 45 will be five-forty (paintalees -- pai/talees), however the exact way to say "five" will change based on the number, as will the exact way to say "forty".
There's not much logic to it -- some tens series are more regular than others -- which means you effectively end up memorizing it, but subconsciously.
Imagine numbers in English but there were three ways of saying each digit, and each number 1-100 would pick from the synonyms. It's basically like that. That is to say, it's not too hard to deal with -- you'll mentally be associating the numbers with their words so it's not hard to say it out, and because they're synonyms not hard to understand when spoken.
In Hindi 40 and 41 use a different word for 40. 51 and 53 use a different word for 50. 55 and 45 use a different word for 5. Plus there are smaller but still significant differences between pretty much every number -- e.g. it's chauBees, but puchees and chauNtees.
NOTE: Hindi has its own script for numbers as well which the article is missed to point out.