What is the ruling on listening to anasheeds (Islamic songs/chants) in which the name of Allah is mentioned, and has Sheikh Ibn Baz issued any prohibition regarding this?

It is permissible to listen to anasheed (Islamic chants) as long as they do not contain forbidden words or musical instruments, or involve imitation of the immoral, or distract a Muslim from his duties. As for the mention of Allah Almighty in anasheed, no scholar has prohibited it per se. There is evidence in the Sunnah indicating its permissibility, such as the hadith of Salama ibn al-Akwa' in the two Sahih collections regarding the Prophet's - peace and blessings be upon him - return from Khaybar, where the Prophet - peace and blessings be upon him - permitted him to chant with the mention and praise of Allah Almighty.