A band's name can be a trademark or service mark if it is used to sell goods or services (e.g., records and performances under the mark). If others were using the mark before you, they might be able to prevent you from using the name as a mark. (By the way, it's advisable to not use actual names in this forum.)
You are asking about symbols and making your mark "differ from the rest". You seem to be asking about the difference between a "word" trademark and a "stylized" or "design" mark. Consider Coca-cola - the letters/words themselves are a word mark but the fancy red/white script version is a stylized mark. But even if you make your mark different by adding symbols, colors, different fonts, etc. to create a stylized mark, you could still have problems with someone who's previously been using a word mark of the same name. You should consult an intellectual property attorney to discuss this point.
You also ask, "How do I go about trademarking my name?" If you are already using the name as a mark in commerce, you may have "common law" trademark rights. If you want to obtain a federal trademark registration, you need to file a federal trademark application. But as suggested above, you may want to talk to an IP attorney to make sure 1) you're not infringing someone else's prior mark or name and 2) that your mark is federally registrable (before you spend the money filing an application).
You can read about basic trademark information here: http://www.uspto.gov/faq/trademarks.jsp#Other006
As my colleague noted, TM rights are acquired by use, and maybe your use of providing musical services pre-dated the use by others - you don't specify dates of use. Recording artists often register their performing name for those services, and the USPTO will do a search of others registered under the same or similar name, to prevent competitors from confusing consumers, which is the USPTO's mission.
There are 2 kinds of TMs, word and stylized marks. Words marks are easier to get but harder to enforce against the use by others. Stylized marks are harder to get but easier to enforce. Which one you may want really depends on what rights you've already acquired by use in whatever type of TM you've been using until now.
You should see a TM lawyer to help you with this - about 1/2 of all TM application are denied, and the fees are non-refundable, and you may want to TM your name for entertainment services, for CDs and DVDs, for clothing, and for online retail, each of which will cost you $325. I don't know whether TMs are rejected because the applicants try to DIY, but it can only help your chances if you hire a lawyer.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Notice: The below is for educational and informational purposes only, is not a reflection on or a representation of any views or opinions held by my employer, and should not be construed as legal advice. Nothing herein is meant to create an attorney-client relationship.
I agree with the other posters and would only add that if, as you say, "other artists or bands are using the name" and it is "a common name," as a practical matter you need to ask yourself if it is a wise business decision to move forward with the same name as a music artist. It might make it more difficult for you to stand out apart from the others. Of course, it is not clear how much time, energy and capital you have invested in building up your name and if you are already well-known by that name in a certain music genre or geographic area. Perhaps you have already built up significant name recognition amongst your fans and others, and it might not make sense for you to choose a different and, perhaps, less common name. Just some additional thoughts.