Okay, say we've created our complete sundial, how would we call the hours?
For that we can best look at the Chorti language. This is one of the languages belonging to the so-called Maya language family.
Mayanists often look at this language that is still spoken in some of the communities in Guatemala, to decipher the hieroglyphs.
I've been looking for words that have some connecting to telling time, focussing on times of day, in an online Chorti-English dictionary that I found here: Chorti

What strikes me is that the Chorti word for hour is hor or or. At first I thought that this was derived from the Spanish word for hour, which is hora. But taking a closer look I saw that the word hor literally means head and is used in combination with other words to mean a great deal of things.

Some interesting time-related words are:

(h)or a k'in	midday, noon
(h) ahk'ab	midnight
"nueve" hor	nine o'clock1
ahk'ab	night, evening, nocturnal
ah k'in	day
sakohbar	morning
tuk'a 'ahr	when, what time, at what time
ek'mar k'in	sunset
wa a t'abaih e k'in	the sun is rising

¹ Probably nowadays the Chorti use Spanish numerals, but in Erik Boot's: A Maya-English Hieroglyphic Vocabulary (online at Mesoweb in pdf format) we can read the classical Maya numerals, so we can use them.