What are the names of numbers in the binary system? The names we use are very much related to the radix we use
$0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9$
zero - one - two - three - four - five - six - seven - eight -nine
We repeat the names
$21$ twenty one, $22$ twenty two .. and so on.
This is not suitable for binary system
If we used the same nomenclature
$1 - \text{one}$
$10 - \text{two}?$
$11 - \text{three}?!$
This is very hard to read and write
Maybe if we used something else it would be very convenient something like:

$1 - \text{John}$
$10 - \text{Watson}$
$11 - \text{Watson John}$
$100 - \text{Kevin}$
$101 - \text{Kevin John}$
$110 - \text{Kevin Watson}$
$111 - \text{Kevin Watson John}$

and so on ..
Is there any official nomenclature? or should I make it up myself?


The names we use are very much related to the radix we use

Etymologically, perhaps, though with some exceptions and inconsistencies as noted already.
The more important point, however, is that the names are used to denote the numbers themselves, not some particular representation of them.
Take for example "two plus three equals five". That's a statement about numbers, which holds true regardless of their representation. All of $2_{10}+3_{10}=5_{10}$ in decimal, or $10_2+11_2=101_2$ in binary or $II + III = V$ in roman numerals represent the same statement "two plus three equals five", and there is no need for different words to describe it depending on the representation.
