I am looking for a word for a period of 10000 years, similar to how millennium represents 1000 years. The closest match I came up with was myriaannum from myria- and annum. However, the metric prefix myria- is no longer used, and in common language, a myriad refers to an indefinitely large number.
The Old Man of the Mountain was formed a myriaannum ago by glaciers.
Is there a more commonly used word for this or is myriaannum my best option?
No, there is no more commonly used word for a period of 10000 years. But I would also advise against using myriaannum; it does not look especially well-formed to me as a classical compound (it combines Greek myria- and Latin annum), and the prefix "myria-" seems to be obsolete in scientific compounds (like mega-annum). In my opinion, it's best to just go with
The Old Man of the Mountain was formed ten millenia ago by glaciers.
Your question, and vickyace's answer, both mention the Greek root myria- which was used with the meaning "ten thousand." But I cannot find any English word derived from this (aside from the aforementioned myriaannum) with the specific meaning "a period of ten thousand years."
I found a Math Forum thread about this topic: Year 10,000? There were lots of miscellaneous suggestions for neologisms of unclear validity, but among these I found the following interesting information in a post by Patrick T. Wahl:
The Greek word "myrioi" for 10,000 is the source of "myrietes" and "myrieteris," which mean "a period of 10,000 years." Similarly, there is "chilieteris," a period of 1,000 years, which uses the "chili-" prefix that became our "kilo-." By the way, there's a very long word for a myriad of myriads = 10^8 in Greek. Nothing like these spellings seems to have entered English.
Classical Latin seems to have had a wealth of "-ennium" words, including some that I didn't suspect ( like triennium, tricennium, tricentennium for periods of 3, 30 and 300 years respectively.) The word "millenium" is the biggest I found. It appears that a modifier got stuck on the front if there was more than a thousand of anything. Something like "decei millenii" for ten millenia seems to be what they used. [...]
Consulting the Oxford English Dictionary, I found no word for "10,000 years" that survived into English. ( Particularly NOT "myriennium" or "myriayore": those are not in the O.E.D. ) I was surprised to find the Greek "chili-" word above as the English word "chiliad." It means "a group of 1000," but also "1000 years." Might "myriad" have the alternate meaning, too? Only a scholar can say, and the O.E.D. gave no citation for such a use.
The entry for μυριετής myrietḗs in Liddell, Scott, and Jones' Greek-English Lexicon confirms that it was used to refer to 10,000-year periods. It seems to have been an adjective rather than a noun.
I would call a 10 millennia time span a decamillennium.
Banzai may refer to: A traditional Japanese exclamation meaning "ten thousand years" of long life.
https://en.m.wikipedia.org/wiki/Banzai
It's not originally English, but lots of English isn't, either.
