The name report system is not automated, although a lot of reports get it to the top of the GM queue faster. It is then reviewed and penalties are issued. Most commonly, you just get a prompt to change the name. A suspension does not happen, usually, on a first offense.
I don’t know what server you were on, but if it was RP then please keep in mind naming restrictions are more restrictive there. It has to fit with the game world.
As others said though, you do want to appeal. Even if it does take the full time of the suspension, you would want it over turned (if possible), so that you don’t have a black mark on your account. Those stack and result in harsher penalties down the road.
For other violations you see, be sure to right click and report those.
EDIT - as to the concern about automation - you would not have that many reports within 20 seconds to trip any automation even if it did exist (not saying it does). More likely you were reported during a prior log in and the penalty was set for the account. When you logged in it applied the penalty. I am only guessing, but that is more likely than getting some insane amount of reports over a name all within 20 seconds.