Yes the Octave is very versatile. I have one instrument that I tune almost as low as a Mandocello, DAEB and then keep capo'd up to GDAE for tunes, with the option of going lower when I want to (in fact I'll be taking delivery of a brand new Buchanan in this tuning as soon as I can go and fetch it).
Going back to the names thing...
IF no-one had ever started using the name Tenor Mandola for the (Alto/proper) Mandola, one could make a case for calling the Octave Mandolin a Tenor Mandola, because all of the family were once defined by their relationship with the Mandola, not the Mandolin, and this pitch is indeed in the tenor range. But sadly the most common use of the Tenor Mandola name is to describe the Mandola, so it's best to just avoid both TM and OM.
Just to confuse matters further Show Off Hams (as they sometimes call themselves) refer to their David Oddy instruments as Mandocellos, when they are also in fact Octave Mandolins tuned GDAD (Tom Napper tunes his Sobel OM this way too).
That idiot Tom Bliss also calls his identical David Oddy instrument a Mandocello, becase Steve and Phil did, and when he made his first album he knew no better, but even worse he tunes his ADGC - in 4ths, which makes it, according to Tom Napper a Picolo Mandobass!