All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
It is permissible – if Allaah wills – to eat that aubergine; the fact that the word “Allaah” is found in it – if we presume that this matter is really true – is not an impediment to eating it. However, if this sister wants to keep it, it is permissible for her to do so as well provided that she protects it from being disrespected.
No evidence is needed to prove the existence of Allaah but seeing such things is something that increases the person’s ‘Eemaan [faith] in Allaah in his heart. Indeed, Allaah is truthful as He Says (what means): {We will show them Our signs in the horizons and within themselves until it becomes clear to them that it [the Quran] is the truth. But is it not sufficient concerning your Lord that He is, over all things, a Witness?} [Quran 41:53]
For more benefit, please refer to Fatwas 81529 and 91019.
Allaah Knows best.