Do I need permission from the NFL, MLB, NCAA, NHL, or NBA to name my food products after them or their players?

Absolutely. All of these sports leagues are extremely aggressive about any unauthorized use of the marks or even trade dress, which could be the colors of their uniforms and team logos. Also, the athletes' (presumably through their agents) are highly aggressive about any use of their name or even likeness that has not been specifically authorized by them. A likeness could be a caricature drawing of the athlete or use of a phrase or slogan popularly associated with the athlete. The leagues probably have people employed full-time just to monitor such unauthorized uses and the sports agents could as well. Whether or not any alleged infringement by these leagues or players are meritorious and would prevail is besides the point because these entities generally have expensive firms working for them that probably will not hesitate to contact you about such unauthorized use. As such, these entities could make undertaking this venture extremely expensive for you if you do not contact the league or player beforehand. I believe some of the leagues may even have one IP firm handling all of the IP matters for all of the teams in that league. Any IP belonging to specific players usually is handled through the players' labor union, e.g. the Major League Baseball Player's Association (MLBPA). THat said, these leagues and players are businesses and recognize the need or value of allowing their name to be associated with certain products (e.g. Campbell soup) as well as using their marks or names to endorse certain non-profit ventures for PR. Therefore, I believe they have some fairly well-established licensing programs and procedures and if you contact them BEFORE any use of the marks or player likenesses, you may find them to be fairly helpful. Also, while I have no idea what kind of licensee fees or compensation may be requested for authorization to use a mark or likeness, I believe the cost may not necessarily be expensive and would certainly be less expensive than dealing with them in a legal dispute. It may be a good idea for you to work with a lawyer before contacting the leagues or players so the lawyer could review and negotiate any proposed license or sponsorship agreements and also to protect you from disclosing your business plan or proposed IP to the leagues without proper protection against their misappropriation of your IP. Good luck.