How to auto fill single line field based on Contact Name entry?

How to auto fill single line field based on Contact Name entry?

Hello Everyone -
I have added a custom single line field in the Task Module called "Contact Company".

I am needing this field to auto-populate with the correlating Company Name of the entered Contact Name field.   (Another words, I enter a name into the Contact Name lookup field, then the Contact Company field auto-fills with that contact's company name)

Yes, the "Related To" field does this already, but I need to relate this field to my Vendors module.  And the Tasks module does not allow Lookup fields to be added.   I have tried to add a formula but I cannot get it to work.

Any help is appreciated.  Thanks!