Kanban boards are mirrors
One of the first steps with Kanban is to map out the current process. A strength of Kanban is that it does not start with an anxiety-inducing upheaval. It starts simply by mapping out the existing process exactly as it stands. The Kanban board is a mirror that reflects the flow of work. What you see may not be pretty, but once the flow is visible, you can gradually make changes to your process to improve things.
A common mistake is to map handovers rather than the states a work item can be in. Individuals often perform several actions on a work item before handing it over to someone else. Mapping these intermediate, finer-grained states makes it easier to identify the exact location of bottlenecks and provides more possibilities for improving flow. For example, by allowing less busy people in the team to shoulder some of the burden.
It's worth emphasizing that a Kanban board with lots of columns does not mean you have to do lots of handovers. A single person may take a work item all the way across the board without any handovers. The intermediate work item states are only made explicit to provide insight. Later, handovers may be introduced but only if they improve flow.
It's also important to note that the states should reflect real states that the work goes through and not states that you think the work "should" go through. New states can be introduced later on, but the first task is to map reality as it is. Sometimes To Do/Doing/Done is as fine-grained as you can go to start with.