So why do あなた think Mello and Near are named that?

That's a good question. The 作者 発言しました he wanted it to be a story to where あなた can speculate unmentioned things for yourself.. so, I'm not sure.

Personally, I think they were both meant to be ironic. Mello, like あなた said, is anything but mello. Near, I think his name is ironic because he's distant from everyone around him- but on another hand, it could also mean that he's always "near the target" therefore always figuring things out.

This is all speculation though.

Hmmm...

I think that Mello's Alias is supposed to be ironic, because he's not calm at all.

Also, for Near's Alias, He's smart, and nice, so maybe it means that あなた always want to be near him.

It's confirmed that "Near" comes from taking the two first letters of his name with the two last letters of his lastname and form a word out of them;
(Na)te Riv(er) -> Near

As for Mello, anyone's guess is as good as mine. He could've gotten his name from Anthony de Mello for all I know.