I didn't understand why you used 'tense-form' if you don't like the term?
You could refer to aspect-stems, which is pretty accurate even if including future-potential, or
tense-stems if you wanted to be quasi traditional but misleading for infinitives and non-indicatives, or
verb category stems if you wanted something more generic.
Just refer to the stems or bases or whatever, rather than the overly generic 'forms'.
As for the verbs themselves, sometimes it depends on definitions of Greek.
For example, γενέσθαι can be viewed as the aorist of εἶναι. (Stephen mentioned suppletion, and some interesting references that I haven't read.)
Some other common verbs include
κεῖσθαι (sometimes this functions in voice-suppletion with τιθέναι)
δεῖν (in senses of obligation)
κάθησθαι (aorist is suppletive καθίσαι)
Then there are the 'funny perfects'
or verbs like
and quasi-rare, quasi-suppletives like
καθεῦδειν (aorist is rare and slightly different root καθευδῆσαι), or
μνημονεύειν (aorist is usually a suppletive μνησθῆναι, very rarely μνημονεῦσαι)
Several of the above need some training at a fluency workshop so that we can attain three-year-old-kid proficiency.
You gotta love Greek.