How to translate my Chinese name to Japanese?

Hi. I had a hard time trying to find out how should my name be pronounced because I am learning Japanese language. I did probe my teacher on it, but she did not say much. If anyone knows how/why. I would need some enlightenment

許國賢 is my name in chinese

The Japanese reading for the individual kanji in your name is:

許　kyo
國 koku
賢 ken

Lately Chinese people living in Japan simply use the original sounds of their names in Chinese, though.

For example, I knew a person whose family name was 黄, and he was referred to as "Hwang-san" by the Japanese colleagues around him (-san is the expression to add politeness when calling someone). He did not use the Japanese reading, which would have been "Ou."

Your name is highly likely to be pronounced like "Kyo Kokken" in a Japanese reading, with a vowel omitted when 國 [koku] and 賢 [ken] are combined.

AK: Lately Chinese people living in Japan simply use the original sounds of their names in Chinese, though.

Well, Japan-based media have been calling Chinese names in Japanese readings, just as Japanese names are called in Chinese readings, but lately some major news media call certain Chinese names based on their own readings.

I assume what each of the three characters means in Japanese is roughly the same as in Chinese.
許 [kyo] : permission, to permit or give.
國 (in an older form) or 国 [koku] / [kuni] : a nation, a country, a province.
賢 [ken] : wisdom, wise.

許 is usually used in a Japanese-origin word or in a kanji compound, not solely as a Japanese word. The same can be said about 賢 .

許す [yurusu] : permit, forgive.
許可 [kyoka] : (official or legal) permission (for someone to do or not to do a certain thing).
許可する : give 許可 .
許諾 [kyodaku] : permission (from the one who has the right).
許諾する : give 許諾 .

賢い or 賢こい [kashikoi] : (evaluated as) wise.
賢しい [sakashii] (when used ironically) : clever, impertinent.
賢者 [kenja] : a wise person.

The character 國 in this form appears in old writings. Its newer form 国 has been used for several decades.
Its most common Japanese-origin reading is [kuni] as in わが国 [waga-kuni] (meaning my country; an expression in a literary style) and 北国 [kitaguni] (meaning a northern province; a compound).
国に帰る [kuni ni kaeru] means to get back to the homeland.
帰国する [kikokusuru] is used only concerning a country.
When a Japanese guy travels for a long distance from his living place in Japan to his homeland in Japan, we may describe it as 国に帰る but not as 帰国する .