White Crane in Chinese / Japanese...

白鶴 means White Crane.

This title directly means “White Crane” in Chinese, but in English, this particular crane is referred to as the “red-crowned crane” or “Grus Japonensis.” This crane is mostly white with a red bill (crown).

白鳥 is the Japanese Kanji and old Korean Hanja title for white swan (Cygnus Bechstein).

The title literally means white-feathered bird. This title can also be used to refer to a white crane.

This can also be the Japanese surname, Hakuchou.

白鶴拳 is the title for the White Crane Fist style of martial arts.

白鶴拳 is also known as “Baihequan” or “Fujian White Crane.”

This is the title for White Crane Karate in Japanese Kanji.

白鶴寺 is the title for White Crane Temple.

You might be looking for 白鹤萻 which is noted as the place where Mrs. Fang Qiniang (founder of the Fujian White Crane style) retired to. But this is really "White Crane Nunnery" rather than temple.

白鶴拳法 means White Crane Kenpo.

This can be romanized as Hakutsuru Kempo or Hakkaku Kenpō in Japanese.

三戦 is a title that literally means “three battles/conflicts/wars.”

三戦 is often figuratively used to relay the idea of a battle to unify the mind, body, and spirit.

Original usage likely comes from Fujian province in Southern China (just across from Taiwan).

This title is used in various schools such as Okinawan Karate, Uechi-Ryū, Gōjū-Ryū, Fujian White Crane, and Five Ancestors among others.

五祖拳 is a martial arts concept (or school) known as Five Ancestors' Fist.

The first character means five.
The second means ancestor, forefather, or grandparents.
The third means fist.

The ancestors referred to by this title and whose attributes contribute to this style are as follows:
1. Grace of the White Crane.
2. Agility of the Monkey.
3. Precision and skill of Emperor Taizu (great mythical ancestor).
4. Power of Luohan (Buddhist arhat).
5. Breath of Damo (founder of Buddhism, or the first Buddha).

南派螳螂 can be translated literally as “Southern School Praying Mantis” or “Southern Style Praying Mantis.”

Despite its name, the Southern Praying Mantis style of Chinese martial arts is unrelated to the Northern Praying Mantis style. Southern Praying Mantis is instead related most closely to fellow Hakka styles such as Dragon and more distantly to the Fujian family of styles that includes Fujian White Crane, Five Ancestors, and Wing Chun.

This style of martial arts focuses more on fighting skills rather than aesthetics.

Of course, you already knew that if you were looking for this term.

Note: This title can be pronounced and does have meaning in Korean but only to Koreans familiar with Chinese martial arts.