How to change to infilll colour of one cell according to another

I am hoping some one can help me, I have started looking to set up a database regarding dates for training, it is dynamic changing the date as the date changes, I have set up a spreadsheet which will highlight cells when a date is overdue (RED), nearly due (yellow)or in date (green). Some Staff have dates that are have all ranges in them completed, nearly due and overdue. I am looking to try and arrange so the staff name will correspond(or infill) to the a colour with overdue taking the priority of colour, and which will change as the priority reduces to yellow and then green as data is entered . this means at a glance I can see who who's name (infill) has training that is overdue or nearly due, rather than looking across the whole of the spreadsheet. this will save so much time.
the cells that change colour are depending whether a date has been reached or not, not based upon a numerical value

Thanking you in advance
Regards James