If your band name is important to you, I strongly suggest you speak to an attorney who specializes in entertainment law. Given your inexperience in this area, you run the risk of forfeiting rights to your name if you do not act properly. Your band name cannot be "trademarked" in any abstract sense. In order to be entitled to trademark protection, your band name must be used as a trademark
Do not hesitate to contact a lawyer as soon as possible.
You need a lawyer that specializes in intellectual property. There are many legal complex legal issues in this area of law and you do not want to move forward without making sure there is no confusion to the public regarding your name.
Generally, this would be sufficiently different, but the devil is in the details. The similarity of the name is not the only factor. There are numerous other ones to consider, most of which likely fall in your favor. See the first link below for the US Patent & Trademark Office guide to its own examiners on the issue:
That your band is not a high school sports team is relevant. The leading case, now 53 years old, on this and still followed widely was one evaluating whether Polarad was likely to be confused with Polaroid, in which the test for differing products with similar names was there stated as:
"...Where the products are different, the prior owner’s chance of success
is a function of many variables: the strength of his mark, the degree of
similarity between the two marks, the proximity of the products, the
likelihood that the prior owner will bridge the gap, actual confusion, and
the reciprocal of defendant’s good faith in adopting its own mark, the
quality of defendant’s product, and the sophistication of the buyers. Even
this extensive catalogue does not exhaust the possibilities – the court may
have to take still other variables into account."
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
You will probably not have any issues regards to this school for the reasons Attorney Burdick aptly noted. Think of Delta Airlines vs Delta faucets. Same exact name, but doing something completely different.
That said, whenever you endeavor into investing in a trademark it is very important that you conduct the proper clearance due diligence upfront and before you submit an application to the USPTO. In the US, this means searching under both federal (USPTO) as well as common law because trademark rights stem from use in this country NOT registration. This means that acquiring a federal registration does not necessarily mean that you are not infringing on another's intellectual property. See the link below for a detailed explanation of the due diligence process and a guide on how to choose a strong trademark.
I suggest that you consult with a lawyer in private and discuss your objectives in more detail. You can start by calling around to several for a free phone consultation, get some insights then pick the best fit to work with.
DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed with the law firm of Natoli-Lapin, LLC on the basis of this posting.
A common theme on AVVO seems to be that a lot of members of the public assume that "Not for profit" means either they (non-profit) will let me walk over them or I (not for profit) can walkover you.