In what circumstances did Romans use diacritical marks, like macrons, in their writing? In particular how common was it to use diacritics in naming letters?
The Romans actually didn't use diacritical marks for the most part. I understand that this question was asked based off of a comment made on a post (which was answered by myself). In my response, I used two diacritical marks: the acute accent (Á) and the macron (ā). These marks are used by modern Latinists to distinguish between long and short vowels, with the acute accent being short and the macron being long. People also use the breve (ă) for short vowels. The breve is only used when the author is not using the acute accent, and needs to distinguish between words spelled the same except for a vowel length. Here is a great website explaining how Romans actually would have written. The written names of letters from your previous post were written using these accent marks, but that was not how a Roman would have most likely written them.
Edit (as per Ben Kovitz's comment)
It indicated that a vowel was long, and was quite common (it was also used above consonants). It originates from the time when vowels were written twice to indicate that they were long. It was a type of shorthand, before becoming widespread. Here is a good image of its usage (look for what looks like scratches angled toward the right above letters).
How this would have been used writing the names of the letters in the alphabet remains unclear.