The spelling for the adjective derived from the name Shaw is Shavian and not Shawian. Similarly you can find Arrow → Arrovian and Harrow → Harrovian. This strikes me as odd.
First of all, I accept that the adjective for /ʃɔː/ is pronounced /ʃɔːvɪən/, so this is not about the word, just the spelling. Now, I see two possible rationales:
Shavian is phonemically closer since v usually represents /v/ in English orthography and w represents /w/.
Shawian is etymologically closer, without being too distant phonemically since /v/ and /w/ are pretty close.
What strikes me about this is that English orthography usually champions etymology over phonemics, in particular when it comes to proper names. Thus, my question is: Has phonemics just won for once, or is there any other argument for spelling these adjectives with a v?