tpcslj, head over to the Copyright section of the forum and read through the postings in the recent thread about using "Anagrams" posted by Taxeon. The topic is similar to the one you have posted here, and there are a few cases cited that you can review, and there is a discussion on the legalities of using the names, likenesses and statistics of sports players.
Tranquility and FlyingRon pretty much summed it all up for you (despite your seeming reluctance to accept what tranquility said, for some odd reason perhaps known only to you).
If you try to capitalize off the names and fame of others, you can find yourself in court. What is involved is copyright law, trademark law, and publicity rights laws. These court battles are expensive to pursue and defend against, regardless of the outcome, especially when you have a large organization like the NFL or MLB involved. They vigorously defend their trademark and publicity rights. They have high-powered attorneys. They have a lot of money. They have a lot of time to spend in court. I am guessing you don't.
Some recent court decisions have leaned toward allowing others to legally use the names and statistics of players for "fantasy" league play. Other decisions have come out in favor of the sports organizations. Others have been settled and the terms of settlement are confidential (google for a Yahoo/NFL suit settled last year).
As for those who sell tee-shirts and other products online that use celebrity names or likenesses or trademarked material on them - they either licensed the use (which is rare) or they will receive a cease and desist letter delivered to them, demanding $$$$$$ for their infringing use, or they will be sued. Some lucky few may escape detection and a letter or a suit only because they
are lucky.
It is a crap shoot, tpcslj - and it can be an expensive crap shoot. Licenses are not granted by these sports organizations often, and they are prohibitively expensive for most people to even consider. The best advice is to read the cases cited in the other thread and this will give you a better understanding of what you may face. Then I recommend you seek out the help of an IP attorney in your area, who can review your plans and advise you on the risks you face should you go ahead with your plans. Then go from there, or rethink your plans.
Good luck.