does it have any religious influence?
Yes, there is a much publicised practice of placing slips of paper containing written prayers into the crevices of the Wall.
Western Wall
There is a much publicised practice of placing slips of paper containing written prayers into the crevices of the Wall. The earliest account of this practice is attributed to Rabbi Chaim ibn Attar, (d. 1743). 
is the western wall in east or west jerusalem West Jerusalem is it known by any other name? Yes, it is known in Islam as the Buraq Wall
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Western Wall [SEP] Prayer notes
There is a much publicised practice of placing slips of paper containing written prayers into the crevices of the Wall. The earliest account of this practice is attributed to Rabbi Chaim ibn Attar, (d. 1743). More than a million notes are placed each year and the opportunity to e-mail notes is offered by a number of organisations. It has become customary for visiting dignitaries to place notes too.