What is the name of a circuit that delays powering of another circuit?
A power supply sequencer or power rail sequencer. This could be done with a simple microcontroller for example, or you could use an analog comparator.

Essentially you want a circuit which has a transistor or other controllable switch for each power rail. When the first rail in the sequence reaches some threshold (e.g. detected with an op-amp or analog comparator), then the switch for the second rail would be turned on, and so on for each rail in turn.

Figure 1 here shows a very basic example of how to start one power rail after another has reached a certain threshold. There are also ICs available which will sequence multiple power rails.