First up: If so many people were going to such lengths to discuss a project of mine in a negative manner, I'd stop to see what I'm doing wrong. While not everyone here is neccesarily super friendly, they all just want to help. It may be a little hard for you believe because of some of the rude statements that were made (yes, I honestly believe some were a bit much), but it's true. Communities don't grow big and strong if they're made up of hateful and mean people.
Second: Calling out specific users and their comments sure as heck isn't good for an image. There are some ways you can vent (for lack of a better word) about them without having an overly negative impact, but being overly defensive and even rude isn't one of them.
Lastly: Justification has its place. You were right to explain the reasoning behind Piku Hachune's nickname being 'the free version of Miku,' but sometimes trying to defend your actions makes things worse. For example, even though you may not have stolen the name Rina Tachibana (don't worry, I believe you), simple defense isn't going to keep people from accusing you in the future. There are some vicious people out there, and they can and will use the fact she shares a name with an anime character to their advantage. A slight name change honestly wouldn't hurt, but if you're fond of her current name then keep it.
Just be aware of the problems it may cause for you in the future.
I don't think you are a bad person, I just believe you are going about this wrong and need some help.