What is the name of this water source for a whole house humidifier?
These are called "saddle valves" or "vampire taps".  They just poke a hole in the pipe with a little pressure around the hole to seal it.  They almost always leak after some time but they are quick and easy to install.

The right way is to cut the pipe and install a tee fitting that then supplies a standard valve.  You can use push-to-fit connectors these days to make the job simple or you can used a traditional soldering approach.

Because of the number of fittings in that small space and the fact that the pipe is damaged with two saddle valves, you'll be replacing that entire bendy section.