If you do mean IUPAC groups 13 and 14, then 14 is rather easy. All form tetravalent compounds, the first three are semiconductors and form hard allotropes and compounds. They could be called semiconductor elements or adamantines (from Gk ἀδαμάντινοc 'hard' < ἀδάμαc, ἀδάμαντοc 'an old name for diamond'). Crystaline carbon, silicon, and germanium are all hard, brittle materials and even tin gives a characteristic 'cry' because of its internal crystal alignment.

A name for group group 13 is more problematic. All except aluminum have a prominent blue or green line in their spectra, but the Greek word for 'blue', κύανοc has already been employed as cyanogen for the compound CN, the precursor of hydrocyanic acid, HCN. It is perhaps interesting to note that the earliest compounds of these elements, borax and alum, were valued for their desiccating properties and as astringents (to this day pickle makers add alum [or grape leaves which naturally contain aluminum compounds] to keep the pickles crunchy). I would suggest xerogens for this property.

There just broadly called early transition metals.

You suspect correctly - the big giveaway clue was when I typed "the boron and carbon groups" :wink:

(Sorry, I still tend to prefer auld Mendelev's roman numeral group numbers than all this IUPAC business ;-)

Perhaps it's just cos they frankly don't have all that much in common with each other?

why not the tricogens and tetrogens easy and understandable, at least for the first few periods. :lol: