Fyodor Petrovich, what is the 'tonic diacritic' that you mention
The acute accent in Νικόλαος. Like Chinese and Norwegian, Ancient Greek was a tonal (or pitch) language.
But it turns out I was wrong. The many h's you see in words with Greek origin are there either because of the letter X/χ (e.g. in psychology) or because of the so-called "rough breathing" (e.g. in hero). Neither of these are written with a separate letter representing the sound /h/ in Greek, the h is added when it's Romanized.
But neither of these cases apply to Νικόλαος, which is written with a simple kappa in Greek, representing the sound /k/.
When I asked the question of where the h came from
here, I got this good answer:
"The original form of the name used in English was "Nicol": it was established before the Norman conquest, usually for monks. Withycombe says the intrusive "h" is found as early as 12C, and goes along with the idea that it probably appeared in the confusion arising from Latinizing of Greek words with the aspirated single letters -- theta, rho, phi, and chi."
So it originally was a mistake, etymologically speaking. Obviously the Normans didnt't always read ch as [tʃ] or [c], but also as [kʰ], since they quite often wrote Nicole (i.e. Lincoln) as Nichole, according to the Anglo-Norman Online Hub.