So why do 당신 think Mello and Near are named that?

That's a good question. The author said he wanted it to be a story to where 당신 can speculate unmentioned things for yourself.. so, I'm not sure.

Personally, I think they were both meant to be ironic. Mello, like 당신 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 당신 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.