When your band or act has any major legal issues hanging over it, that usually will stop the band from being considered for contracts with managers, agents, labels, etc. Questions about ownership of the name are a huge legal issue. The best step you can take is to start your new band with a new name that is not now and has not in the past been the name of a band anywhere in the world. Start researching. Google is a good start.
Once you pick the name, contact a lawyer to do a search and register trademark on the name. This is work I do, and I think it is an excellent investment for a band. NEVER use an online pseudo-legal service to try to register trademark on a name. Trademark registration is a complex process that takes over a year to complete. Those online services are not lawyers and they simply fill out the application, probably incorrectly. The application is merely the beginning of the process. There is still a year or more of legal work after that. If you use one of those fake legal services online, you will be out the money you paid, which at this time will be over $400, and you may also lose the right to use the name. Just use a real lawyer for your legal work.
Most bands that go on to become famous go through many personnel changes. That's just how it is. Bands break up because of differing levels of commitment, differing levels of talent, artistic differences, personality clashes, power plays, drug and alcohol use, mental and emotional instability, jobs, school, and family changes. The band itself can have stability and longevity, even as the members come and go. It takes some solid planning and foresight to make that happen.
A band name does have value to it, and goodwill attached to it. That means people recognize the name and will go to shows and buy CDs or downloads because they associate good things with the name. Therefore, who has the right to use the name is a very important question.
Since you did not form a written contract with the first band, the band is probably considered a de facto partnership. That is if you all joined at about the same time and were all considered partners. If that is the case, the assets of the band would be divided equally. The band name is one of the band assets. Since you cannot divide a name, none of you can use it unless you get permission from the others. If it is worth money to use the name, you might consider making a money offer and then getting a written contract about use of the name. Otherwise, you are truly best starting new and fresh and coming up with a totally new name that is not being used by any other band anywhere else in the world. And, if you have other assets that must be divided, such as shared recordings, you should definitely consult with a lawyer who does this sort of music work.
As you form your new band, with a new start, I strongly advise that you get a band contract written up to address such things as band name, song ownership, recording ownership, personnel changes, ownership of email lists and social media accounts, ownership of music sales accounts, and many other factors. Some people like the drama and magic of forming a band without advance planning. This is similar to falling in love and diving head first into a relationship. However, the magic quickly wears off and the drama remains and is intensified. Think of a band contract as a prenup.