U.S. District Courts are generally known as
The United States District Court for the X District of Y
where X is "Northern," "Southern," "Eastern," "Western," "Middle," or nothing at all, and where Y is the name of the jurisdiction (e.g., Alaska, Texas, Guam, and the like).
Which currently operational U.S. District Courts do not precisely fit this pattern? Partial credit will not be given.
UPDATE: Note that the question is limited (three times!) to U.S. District Courts. If the court you're thinking of isn't a U.S. District Court, it doesn't qualify. If you think some court that isn't called a U.S. District Court is actually a U.S. District Court, please explain your position in any comment you post.
FURTHER UPDATE: If you think some court qualifies because of its nonstandard name -- for instance, one commenter suggests the "Connecticut District Court" -- please point to some evidence that the court is actually called that. The United States District Court for the District of Connecticut, for example, actually seems to be called the United States District Court for the District of Connecticut -- which fits the standard format described above -- and not the Connecticut District Court.