I believe once upon a time that h used to be silent, and therefore historical sounded like it started with a vowel, so you'd have said "an istoric....". Even after the h started to be pronounced the "an" remained. As time passed, people began to realise this was absurd, and so in modern English you will now increasingly find "a historic". If you hear or read someone say "an historic..." they're following older rules/practices and as Adam said, they sound utterly pretentious. You should always say "a historic" unless you want to be lumped in with a pretentious lot of people who are sticking to outdated grammar conventions that genuinely no longer apply.

This is a strange historical thing. In previous times, the "h" in "historic" might or might not be pronounced as we pronounce it today. In some cases, as spoken by some speakers, it sounded more like 'istoric. We choose an/a based on the actual sound that follows, not what letter we use to write it. Thus, "an 'istoric". Some people---especially strange, pretentious people---continue doing this to this day for no good reason unless they perhaps think it is correct still because it was historically correct. (I'm sorry to any pretentious person reading this who still says "an historic monument" etc. :) )

Both "a historical identity" and "an historical identity" are grammatically correct, but the use of "an" before "historical" is more commonly used in British English. In American English, "a" is typically used before "historical". The choice between "a" and "an" depends on the pronunciation of the word following the article. If the word following the article begins with a vowel sound, "an" is used, otherwise, "a" is used. In the case of "historical", some people pronounce the "h" sound, while others do not. Those who do not pronounce the "h" sound would use "an", while those who do pronounce the "h" sound would use "a". So, it ultimately depends on your personal preference and the style guide you are following.

Usage varies. "An historical..." was once common, but is now rare. "A" versus "an" is based on the sound of the start of the next word. The "h" at the beginning of the word "historical" is sounded very lightly. Depending on the century, the country, the social class etc. of the speaker it may be almost silent. My feeling is that a speaker will say "a historical" if, in his head, they imagine that the h is clearly audible, and "an historical" if it is not. In real life, published English often conforms to a reference book called a "style guide." The publisher decides what style guide to use. A common one in the United States is the University of Chicago style guide. A web search for "chicago style guide an historical versus a historical" brought up a detailed article which says: "In Chicago style, it’s _a_ historical novel. Please see CMOS 5.74: “With the indefinite article, the choice of _a_ or an depends on the sound of the word it precedes. _A_ precedes words with a consonant sound, including /y/, /h/, and /w/, no matter how the word is spelled {a eulogy} {a historic occasion} {a onetime pass}. _An_ comes before words with a vowel sound {an FBI agent} {an X-Files episode} {an hour ago}.”