What is the opinion of Sharia on hanging signs bearing the name of Allah and the name of the Prophet, peace and blessings be upon him, in front of worshippers in the mosque? And do these signs distract worshippers from their prayers?

It is disliked to place anything that distracts a worshiper in the direction of the qiblah in the mosque, due to what was reported from the Prophet (peace and blessings be upon him) regarding removing anything that preoccupies the mind during prayer, such as the decorated curtain (qiram) whose images he saw during his prayer, and his covering of the ram's horns in the Kaaba; because they distract the worshiper.

As for placing plaques or vessels inscribed with the majestic name "Allah" and next to it "Muhammad," this is not permissible, due to the exaggeration it contains regarding the Prophet (peace and blessings be upon him) and equating him with Allah, and this is a means to shirk (polytheism).