Why are the posterior and anterior inferior temporal cortex called area TEO and area TE respectively?
These are very old names for primate cortical areas, originally from the anatomist Constantin von Economo and also used by von Bonin and Bailey (1947) (where the TEO region name seems to originate).

Like Brodmann areas these regions were defined by cytoarchitecture well before most functions were determined.

I discovered another work that I can access from 1935, Rose (1935) that is quite helpful for the TE terminology. From Rose it is clear that von Economo labeled areas in the temporal lobe TA, TB, TC, etc. up to TH. So they seem to be simply "temporal"+letters of the alphabet. Rose refers to "Area temporalis propria" as area TE, comprised of Brodmann areas 21 and 20; Rose calls Brodmann 21 "TE1" and Brodmann 20 "TE2" which are separated based on the size of layer 3 pyramidal cells.

As far as the TEO terminology, Boussaoud et al (1991) write:


  In their study of  the cytoarchitecture of  macaque cortex, von Bonin and Bailey ('47) labeled this region with a question mark on their section drawings but showed a photomicrograph through the region that they labeled  “TEO.”


This is the best evidence I can find that the TEO name a) originated with von Bonin and Bailey, and b) that the further origin or meaning of the name is unclear; it's just a label on a photomicrograph that wasn't even used in the drawings by those authors who instead used a ?. I suspect further authors preferred the TEO terminology rather than confusingly referring to "area ?" and yet they felt like giving credit to von Bonin and Bailey for their work on the macaque cortex.

It's unclear to me whether TEO is meant to be an acronym; "temporal" is part of the name, but whether O stands for a word (perhaps occipital, as it is toward the occipital lobe?) or if it is actually the number 0, or a non-English word (possibly German or Latin?). However, when more modern neuroscientists refer to area TE and area TEO, they are simply intending to refer to "area TE and area TEO in the von Economo/von Bonin &amp; Bailey terminology."

Other terminology, such as referring to posterior or anterior inferior temporal cortex, may seem more descriptive but there isn't anything inherently wrong with referring to the older names as long as people know what area you refer to. TE and TEO are clear, short names that have been used for decades, whereas inventing a new acronym like PIT or AIT would be unfamiliar at this point.

References

Boussaoud, D., Desimone, R., &amp; Ungerleider, L. G. (1991). Visual topography of area TEO in the macaque. Journal of Comparative Neurology, 306(4), 554-575.

Rose, M. (1935). Cytoarchitektonik und Myeloarchitektonik der Großhirnrinde. Handbuch der Neurologie, 1, 588-778.

von Bonin, G., &amp; Bailey, P. (1947). The neocortex of Macaca mulatta.(Illinois Monogr. med. Sci., 5, No. 4.).

von Economo, C. F., &amp; Koskinas, G. N. (1925). Die cytoarchitektonik der hirnrinde des erwachsenen menschen. J. Springer.