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 ‘alayhi wa sallam, is His slave and Messenger.
There are two aspects to the issue of writing the names of Allaah The Almighty on shopping bags: the ruling of this writing and the ruling of desecrating this writing through trashing the bags or putting them in unclean places. Writing on them is permissible as long as it is known that the bags would not be disrespected or thrown away.
Disrespecting them is unlawful whether the writing is in Arabic, English or any other language. It is impermissible for anyone who knows that it is the name of Allaah to do so. Intentional disrespect for the name of Allaah is considered disbelief in Him.
Allaah Knows best.