Some discussion over the identity of Nemo's little octopus friend Pearl has led me into a deep investigation of Grimpoteuthis (dumbo octopuses) and Opisthoteuthis (flapjack octopuses). Both are shortened on the antero-posteral axis (which, yes, takes some head-scratching to figure out--octopuses are even more difficult than squid when it comes to axes of symmetry) but this shortening is carried to the greatest extreme in flapjacks. Hence the name. From the Tree of Life web project:

Most species of Grimpoteuthis [dumbos] are poorly known. They are somewhat less compressed in the anterior-posterior axis than are members of Opisthoteuthis [flapjacks] and they generally have relatively larger fins.

However, intra-generic variety is considerable. By which I mean: each genus contains a number of different species, some more squashed than others. Since Pearl's antero-posteral flattening is minimal, I maintain that
she's a dumbo, but we may never know definitively which octopus
inspired her artists.

Grimpoteuthis and Opisthoteuthis belong to the same octopod family, Opisthoteuthidae, which contains three other genera of deep-sea octopods: Cirroctopus, Luteuthis, and Cryptoteuthis. (Since "teuthis" technically means squid, only one of these names isn't a misnomer, but, well, there you go.)

Unlike the dumbos and flapjacks, none of these three genera have common names, so here are my humble suggestions:

Cirroctopus:

Freaktopus
(Yeah, it's a little bit on the grotesque side, but that's the fault of the fixative more than anything.)

Luteuthis:

Braintopus

And my personal favorite, Cryptoteuthis:



The head crab!

(See, this was the conversation that just happened in my house:
Me: Look at this freaky cephalopod!
Spouse: AHHH HEAD CRAB AHHHH.
Me, vaguely disturbed: What is a head crab!
Spouse: They are from a game called Half Life.
Me: Oh, I think I saw those on Penny Arcade.

Indeed, the resemblance is uncanny:
)