Is it true that on the Day of Resurrection, Allah will call people by their names and their mothers' names, and what is the response to this statement, and is there any Shar'i (Islamic legal) evidence for it?

The saying that people will be called on the Day of Resurrection by their mothers' names is incorrect. The correct view, as indicated by sound and explicit Sunnah (definition), is that they will be called by their fathers' names. The proof for this is the Prophet's (peace be upon him) saying: "Indeed, for every betrayer, a banner will be raised on the Day of Resurrection, and it will be said: 'This is the betrayal of so-and-so, son of so-and-so.'" And his (peace be upon him) saying: "Indeed, you will be called on the Day of Resurrection by your names and your fathers' names, so make your names good." As for the hadith (definition), "O so-and-so, son of so-and-so," it is weak. And as for some people's interpretation of the verse: "On the Day We shall call every people with their Imam" (17:71) to support this weak saying, it is one of the Bid'ah (innovations) in interpretations.