Is it permissible to give one's name and mother's name to someone who offers assistance by reciting Quranic verses with the intention of facilitating marriage, while claiming to possess insight and to do nothing but (what is in) the Qur’an?

If the raqi (exorcist) asks for your name and your mother's name, that is a sign that he is one of the soothsayers or charlatans, even if he recites something from the Qur'an. It is not permissible to seek his help. The Prophet, peace and blessings be upon him, forbade going to soothsayers and said: "Whoever goes to a soothsayer and asks him about something, his prayer will not be accepted for forty nights."

You must have a good opinion of Allah, rely upon Him, and frequently engage in prayer, supplication, and remembrance. Use the legitimate ruqyah (definition) (incantation), for the Prophet, peace and blessings be upon him, said: "Whoever is afflicted by poverty and refers it to Allah, Allah will soon provide for him with immediate or delayed sustenance."