Adding a parent company at the Lead stage

Adding a parent company at the Lead stage

Hi
Many of the organisations that we work with have parent companies. 
We would like to have a clear view all the way through the system that makes reference to the parent company. Are you able to add this in the leads stage? Would it make sense to? . 

We feel there are there are 3 stages to consider - a Lead that can then become a Prospect (a potential client) until such time work has taken place then move to becoming a Client.
What is the best way to manage a prospect within the CRM system.

Any thoughts or suggestions would be appreciated.

Thank you 
Richard