[Serious Question] What is the official name for the practice of capitalizing divine pronouns?

I don't know, but now I am curious too. I will see what I can find out.

Excellent question.

Well, a quick pass through what the net has to say.

Capitalizing the H is not a requirement, some Bibles don't do it, and the ones that do are not consistent. When it is done, it is done for two reasons.

1-as a sign of respect for the divine name it is substituting for

2- to set the god He apart from another male in the sentence or story.

I didn't find a name for it, but I may ask my rabbi friend about it. I just love a good puzzle.

Another EDIT My rabbi friend said it's a Christian thing, no capital letters in ancient Hebrew, so, it is a relatively new thing, and I am out of ideas on who to ask.

This grammarian doesn't use any special term to call it.

God is capitalized when it functions as a name. In this use, God is a proper noun like any other name and does not take a definite or indefinite article. But in phrases like the Biblical god and a forgiving god, which do have articles, there’s no need to capitalize god because it is a common noun rather than a name—yet many religiously inclined writers still capitalize the word in these instances.

When the noun god is used generically, especially in reference to a non-Biblical god, it is not capitalized.

English speakers also traditionally capitalize the pronoun He in reference to God. This remains a common practice among people of faith, but it is by no means obligatory.

In phrases like for God’s sake, by God, and thank God, the word is capitalized because it generally refers to the god of the Bible and treats the word as a name.

http://grammarist.com/style/god-capitalization/

There is a bit more to read if you follow the link.

"capitalization"

http://www.chicagomanualofstyle.org/qanda/data/faq...

Note that it is also done in English literature in some non-divine situations, such as when referring to royalty, to non-royal high-ranking officials, to institutions, even to ships, etc.

It is, basically, done whenever the author wishes to display a special degree of respect to someone or something.

Yes. It shows God's respect from us, even thought His name is not used.