Why should it be like this,instead of maybe 'Adachi's leak','Adachi leaks' or 'Adachi leaked'.
I read this report on San Francisco Chronicle.
A similar example is 'Journalist Says Police, Feds Raid Home in Pursuit of Adachi Leak Information.'
Here are the links.
Journalist Says Police, Feds Raid Home in Pursuit of Adachi Leak Information
Specifically,should i paraphrase 'Adachi Leak Information' into 'Information leaked by Adachi' ,or 'Information about Adachi Leak'?
It wouldn't be "Adachi's leak", or "Adachi leaked/leaks" because the "leak" is related to Adachi, but Adachi did not do the "leaking". It was a leak, perpetrated by others, of information about Mr. Adachi.
This is "Headline-ese", a special form of English used in newspaper headlines etc. Its purpose is to convey intriguing information, as briefly and enticingly (to get you to buy the paper) as possible. The usual rules of grammar are sometimes suspended, and stacking multiple nouns all in a row is a common characteristic of this style.
So the 3 nouns, "Adachi Leak Information", mean "information about the leak [unauthorized release] (of the contents of a report) pertaining to (the death of) Mr. Adachi".
"Leak" is a noun here. "Adachi" is acting as a modifier on that noun. This is like a headline about a big storm: "Hurricane!" or a global conflict: "War." Either of which could be modified: "Massive Hurricane" ......."Trade War"
