Is it permissible for someone whom Allah has taught His Greatest Name to invoke it for worldly needs, with clarification of the Hadith of Aisha and the narration of Rabia Al-Adawiyya's supplication with it for victory?

It is permissible to supplicate with Allah's Greatest Name for worldly matters. The Hadith you mentioned concerning Aisha in this regard is weak and not authentic, and thus cannot be used as proof for the impermissibility of supplicating with it for worldly matters, as it contradicts authentic evidence that permits it. As for the narration of Rabia al-Adawiyya, it has not been reviewed.