Do you need a purpose to exist?
No, not really. I don't really believe that everything has a purpose in the first place, so why should I even start to think that I have a purpose.

Do you need a reason to live?
Nope. I just go with the flow until I catch the bus (ASBS reference).

Do people need to know who you are for you to exist?
No. If you exist, then you exist. Even if you have no social life, if you are paying bills, then you exist. I mean, the electric companies are getting money from someone, right?

Can you live with being a nobody?(Not KH Nobodies)
Most people seem to be, so sure. Although, my definition of nobody is anyone who is normal or below those standards. If you are famous, part of a big company, or the like, then you are not a nobody.

Can you exist with being ignored by the masses?
Eh, I've probably experienced worse things.

Do you need recognition to think you even reside in this plane of existence?
Nope. I'm here, aren't I? Therefore, I exist. It doesn't matter what plane.

If you weren't recognized by anyone, would you cease to exist?
Nope.

If your purpose was fulfilled, would you continue to live?
Pretty much. Until I got killed, anyway.

Would you even have a reason to?
Nope.