I honestly wouldn't be able to explain exactly why Kaname, but I do tend to have a pattern for which characters I end up obsessing over and those I don't.

As soon as I read Obbligato I fell in love, as soon as I knew HiMERU wasn't really HiMERU, I wanted--YEARNED to know more and oh boy I didn't regret the tears at all!
Kaname is quite literally a reflection of HiMERU, the persona he's created. While the explanation given is that Reimei SP students are told to make a persona/have a stage name, I do believe the creation of HiMERU stems from much deeper than that

Kaname is, simply put, extremely flawed: he pretends to be smart but isn't, is short-tempered, loud, childish and rude, everything that HiMERU isn't. HiMERU is merely a mask to veil all of his insecurities behind, to pretend to be someone he's not--just like his brother is doing today.

So on the psychological side of things, I love that baby a lot. But I seem to have a weakness for what I like to 'bitchbabies' or well, characters that either pretend to be smartasses, or actually are smartasses but quite rude about it. In general, flawed characters that yearn to do better/overcome trauma are also charas I'm drawn to for the heart-breaking angsty aspect they can bring to a story!