We’d recommend against using the names of basketball teams for fundraising purposes. It’s possible that NCAA or NBA trademark owners would not know (or care) about your use of team trademarks. After all, their primary battle is against counterfeit merchandise manufacturers. But, in the event that the teams do care and consumers are likely to be confused into believing that a basketball team endorses or is associated with your nonprofit, then your use violates trademark law and the trademark owners can demand you stop. You might argue that fundraisers and contributors are sophisticated enough to minimize the likelihood of confusion. That is they understand that NBA and NCAA teams are not associated with your nonprofit. But this is a longshot strategy and we imagine you don't want to defend yourself in a lawsuit.
Why not fair use? "Fair use" is a copyright defense and doesn't apply to trademark disputes. (There is a trademark “fair use” defense but it is also not applicable to your situation.) If you want to disregard our advice and go ahead with your plan, you might consider a prominent disclaimer to the effect that the NBA and NCAA do not endorse, and are not associated with your use. Keep in mind that disclaimers have little value when used incorrectly.