I want to list the names of all my best friends on a paper, and it needs an title. Which one is correct: "Best Friends List" or "Best Friend List".
You answered your own question :) :
list the names of all my best friends
In other words, should a "list of X's" be called an "X list" or an "X's list"? I don't think there is a definite correct answer here; either could be acceptable. However, I think the singular construction is more common.
If I were making a list of tasks, I would probablty call it a "task list". I notice that Facebook features "friend lists", not "friends lists". The list of tracks on an album is generally called a "track list".
On the other hand, I have a hard time thinking of examples of the other format, where a "list of X's" is called an "X's list". Putting both "priority lists" and "priorities list" into Google, they both have lots of hits, but the singular version has more than 10 times as many as the plural version. Neither sounds horrible, but "priority list" is clearly more common, at least on the Internet.
Just an aside, "best" is a superlative. There can only be one. So technically, a list of "best" is extremely short (one entry, which might not be called a list). However, the term is used loosely when referring to friends, so let's ignore that.
There are two other answers so far, pointing in opposite directions. Both can be right because there are two possible perspectives.
"Best friends" can be used as a descriptive term for a group of people. If you have a list of the group members, you can call it a "best friends list". The list contains the members of the "best friends" group.
"Best friend" can also be used to characterize specific individuals, a "label" for a person. In that case, you could call it a "best friend list". The list would be a compilation of individuals who are a "best friend". This would be analogous to G Tony Jacobs's example of a task list. A "task" is a type of activity and a task list would be a collection of such activities.
This is a case where either usage can be correct, depending on your context. Popularity of one vs. the other doesn't really tell you much about correct vs. incorrect, it only indicates which context is used more often.