associated

Since the mid-fourth century until era of  the early the Tang dynasty.
Era of three Kingdoms had been going on at the Korean Peninsula.

Most powerful country in those was "the Koguryo dynasty" in the north. (高句麗)
Japanese pronunciation of 高句麗 is ”Kōkuri".　

Also the Koguryo dynasty had been referred to as 高麗 from China and Japan.
(There seems to be such a representation to government documents at the time.)　
And this 高麗 seems to had meaning the Korean Peninsula in Japan.　
　
Japanese pronunciation of 高麗 is ”Kōrai".


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By the way，this 高麗 is also pronounced "Koma" in Japan.

And in Japan，There is a place that has place name 高麗.
In this case，this Chinese character is pronounced "Koma".
　
And peoples who came to Japan from the Korean Peninsula.
They seem to have been called 高麗.
Probably，as it "Koma"，not "Kōrai".　
　
"高麗・koma" of place name.
These seems to be attached to land they had settled.
　
Currently, there are ”Komae” city in western Tokyo. (狛江)
Pronunciation of ”狛” of the Chinese characters in Japan is ”koma”.

狛江 also seems to have been settlements of people of koma originally.　
　
　
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First，komae was a representation of the place name as 高麗江.
It was converted to 狛江.
It is said to be so.
　
But word of koma existed in japan originally as a word that indicates the people of Korean Peninsula.
　
高麗 and 狛 of Chinese characters.
Later，those did associated to koma.
Just maybe，there may be this.　

Incidentally，the entrance of the shrine of Japan.　
There is a statue of two dogs.

These dogs has a meaning of talisman against evil.

They are referred to as "Koma inu". (狛犬)
Its meaning is the dog of koma.