What is the ruling on registering with companies that take the names of those wishing to work for them to carry out their tasks, and pay them a monthly wage under a contract, with their consent that they do not have to be physically present or directly involved in the work?

If companies employ workers in your name and pay you a known wage, this is permissible if the laws of the country do not prohibit it. This is considered a rental of a license, which is an intangible right that may be compensated for by sale or lease, provided it is free from uncertainty (gharar), deception (tadlees), and violation of the ruler's authority. However, if they employ you to achieve a quota for citizen employment without assigning you work, then other fatwas on this matter should be consulted.