Is it a problem if a company that sells electronics and an independent rock band share exactly the same name?

I assume that you are asking whether trademark law would bar one of the parties from using the name.  The answer is probably not under U.S. law (I  have no idea whether Japanese law is the same or similar.) The idea of exclusive use of a trademark is to avoid consumer confusion, and to prevent one party from cashing in on goodwill which another party has invested time and money to develop.  For example, you can't operate a hamburger stand called "McDonald", because it is confusingly similar to "McDonald's"; customers would think your business was affiliated with "McDonald's" and you would be trading on the value of the "McDonald's" name, which it has spent a lot of time and money building up.   However, the prohibition generally applies only to businesses operating in the same field, otherwise there is no confusion or misappropriation.  There would be no trademark issue if you opened a garage called "McDonald's"; no reasonable consumer would believe that you were affiliated with the restaurant chain, and you would get no benefit from its goodwill.  Based on what you've written above, the same would probably be true of the electronics seller and the band.