Is time created by movement through a higher dimensional object?
No. Time isn't actually "created" per se. And there is no movement through a higher-dimensional object. The block universe that people talk about models space at all times, so there's no motion in it or through it. However it's reasonable to say time is the result of motion through space. If you think about a clock, what it actually does is "clocks up" some kind of regular cyclical motion. This might be the motion of a pendulum, the motion of a rocker and cogs and gears, or the vibration of a quartz crystal. The inner mechanism of a clock is called a movement for good reason. The thing we call the time is effectively a cumulative measure of this movement, suitably displayed. Time is a dimension in the sense of measure, not in the sense of freedom of movement. I can hop forward a metre but you can't hop forwards a second.
In a comment I read on this page, someone mentions a theory where time is created by moving through and slicing "moments" of a higher dimensional object. For analogy, a 2-D creature living on a plane that moves through a 3-D object may experience the different slices of the 3-D object as "the passage of time" in their 2-D world.
It sounds like a garbled version of Eternalism, see Wikipedia:
"Eternalism is a philosophical approach to the ontological nature of time, which takes the view that all points in time are equally "real", as opposed to the presentist idea that only the present is real and the growing block universe theory of time in which the past and present are real while the future is not. Modern advocates often take inspiration from the way time is modelled as a dimension in the theory of relativity, giving time a similar ontology to that of space (although the basic idea dates back at least to McTaggart's B-Theory of time, first published in The Unreality of Time in 1908, only three years after the first paper on relativity). This would mean that time is just another dimension, that future events are "already there", and that there is no objective flow of time. It is sometimes referred to as the "block time" or "block universe" theory due to its description of space-time as an unchanging four-dimensional "block", as opposed to the view of the world as a three-dimensional space modulated by the passage of time".
Is this idea well developed in physics?
I struggle to answer that. Eternalism and the block universe have been around for a long time, but there's no evidence at all of any 3D object moving through some higher-dimensional 4D object. The patent blatant evidence is that we live in a world of space and motion. This is modelled using spacetime, but the map is not the territory. You can't point up to the clear night sky and say "hey look, there's a worldline".
Can you share the name of this idea so that I can find it on google?
Eternalism is probably what you're looking for, and the growing black universe too, which mentions the spotlight. But I would encourage you to look into A World without Time: The Forgotten Legacy of Godel and Einstein. This concerns the opposite viewpoint which is called Presentism. Most people will tell you that Einstein and relativity is all about eternalism, but it isn't, it's all about presentism, because Einstein wrote equations of motion, not the equations of a static block universe.
Also, could dark matter play a role in this process?
No, sorry, dark matter is nothing to do with it.