Why is it that Kitty is never referred to by her codename....like ever. It's like they totally forgot she was Shadowcat. Did I miss something where she said she didn't want a codename anymore or something? It really bothers me that they refer to her as Kitty Pryde all the time.

Its cause at that the moment she isn't a Superhero. In fact, she has done any thing heroic for nearly three years now... If she had died, I'm sure she'd of still been refered to as Shadowcat by the writers... But yeah.

For the same reason of Jean Grey and Emma Frost.

Now that I think it through Rachel was suposed to be Marvel Girl now, but still everyone seems to call her Rachel Summers.
 
Another example is Moonstar. It's her lastname after all.

She earned the moniker "Shadowcat" after her martial arts training. They really haven't explored her sweet ninja moves in a while...maybe she forgot them and has to get back in the swing before she feels comfy with that name again.

All of the mini series that featured Kitty by name didn't use her codename.  It wasn't Shadowcat Agent of SHIELD, or Shadowcat & Pete Wisdom...  It's not really her official codename any more. 
 
Personally, I liked it in Wolverine & The X-Men, how she was simply called Pryde out in the field.

" I think because she's more of the "people's mutant" now she's back on the X-Men, but she's their poster child for loveable mutants everywhere so I think it makes her more relatable to be Kitty Pryde, and not another superhero with a codename just my thought, of course, she could come back as Shadowcat before it's all said and done "

Also as at least one of her parents( father Carmen Pryde) is apparently dead and her mother Theresa is out of the picture, she can afford to "go public" with her secret identity such as Captain America and Iron Man along with the FF have long been "out of the closet"( the comparison to homosexuality , bisexuality or lesbian is NO coincidence). in addition to looking like the "girl next door"( unlike say Wolverine, Rogue, Nightcrawler and most of all Magneto), I suspect that her Jewishness(admittedly understated by her) provides an extra level of immunity from anti-mutant prejudice- few people will wish to be seen as the intellectual or moral descendants of not just Rev. Stryker, the Friends Of Humanity but the Third Reich itself!

Terry

There is also another reason for being known primarily by her real name to the general public as opposed to her "superhero"code name I think and it has to do with being the "poster girl" for mutant rights- true, there are some mutants who are "out of the closet" (Iceman, Beast, Archangel, Quicksilver the Scarlet Witch) as are some "normal" heroes(Iron Man, Captain America, the Fantastic Four who have been out since their inception by Susan Richards own admission and it has NEVER been a big deal) but most mutant superheroes such as the X-Men are pretty much an unknown quantity. Given the prevailing fear and hatred of mutants, I think Kitty can do more good for mutantkind as a public advocate for her people( if mutantkind can be said to be a people in its own right) than simply fighting baddies as an X-Man!