Is it permissible to take money from the government under the name of family or child assistance?

There is no harm in accepting government assistance if you meet the stated conditions, without deception or lying. The proof of its permissibility is what Al-Bukhari and Muslim narrated from Umar, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, said to him: "(Take it, use it for your needs and give charity from it. Whatever comes to you from this wealth, while you are neither covetous nor begging, then take it. Otherwise, do not let yourself desire it.)" It is permissible to accept it whether the government is Muslim or non-Muslim, as long as it does not entail compromising any aspect of one's religion.