Not necessarily. It would depend on the type of release really i.e. commercial or free, digital or physical. If you want to earn money from your work, you could sell on bandcamp or similar service providers, who let you stay completely anonymous besides an E-Mail for signing up. If you want to perform for an audience, the host will probably want to know your name and some form of contact info.
If you want royalties (your track played publicly on radio stations, TV, etc.) you will want to hook up with a PRO (Public Performance Organization), the biggest for the US are ASCAP, BMI and SESAC. If you live in another country, here in Germany we have the GEMA and the GVL, who basically collect money from airplay for you. Releasing physical albums, admitting your real name to the record label is mandatory, it doesn't have to appear on the release (booklet etc.) though.
You do have the option to found a company, which can act as your strawman, thus concealing your true identity, which is common practice in the music industry.
So, long story short, you can be pretty anonymous for the public, but as soon as money starts to flow, organizations will need to know your real name for tax purposes.
