So do we know how the Romans pronounced the names of the letters? If a Roman asked a friend how to write the number fifty-four, how would the friend reply?
Does the question really come down to “Did the Romans have names for the letters of the alphabet they used? And, if so, did they have different names for those letters when they were used as numerals?”
According to the Wikepedia article on the Latin alphabet, the Romans did have names for their letters. I was “i”, pronounced like the vowel sound in “sweet”; V was “u”, pronounced like the vowel sound in “shoot”; X was “ix”, pronounced “iks”; L was “el”, pronounced pretty much as you would expect; M was “em”, pronounced likewise; C was “ce”, pronounced with a hard ‘c’ and the vowel sound from “dress”; D was “de”, also with the vowel sound from “dress”.
There must be a degree of conjecture about the pronunciations; there must have been some degree of variation both over time and in different places.
Wikipedia doesn’t discuss whether the letter were given different names when used as numerals, but there seems no obvious reason why this would have been done.
Roman numerals were originally not derived from, nor related to, the letters that they eventually became associated with. I would expect that before the numerals became associated with letters, the symbols for the numerals would not have been pronounced like the letter names.