As Oldiesmann mentions it was chosen because of its lightweight nature, especially the v0.9.8(I think?), when compared to Joomla or even Wordpress solutions. We did discuss a few years later on changing the name becasue it was well, not "tiny" anymore. On the other hand SimplePortal wasn't quite "simple" either(it has quite a few features).
I did suggest at that time to rename it "TPortal", mainly because the code has lots of functions named "tportal_"..but ultimately it didn't say anything about the script as much as "TinyPortal" did - even if its a bit misleading.
Nowadays I think it should keep the historical name since its become a household name of sorts..and because it really should be majorly rewritten/feature-changed to change the main name. IMHO anyway.