Techdirt reports on this issue, and also that MLB is also still trying to claim ownership over game statistics, even though facts cannot be copyrighted.
Little League teams should tell MLB to take a hike.
UPDATE (June 2, 2008): The Supreme Court denied cert on MLB's lawsuit against C.B.C. Distribution and Marketing for its use of the names of MLB players and statistics for fantasy baseball, without a license from MLB. The court of appeals in St. Louis had already ruled that C.B.C. has a free speech right to use player names and statistics, which have previously been regarded as facts not subject to copyright. Some have worried that this ruling will endanger licensing arrangements regarding the use of celebrity names, but cases that involve an endorsement of a product seem to me to be clearly distinguishable from this case.