You can see all the important information about your companion in its overview. You can access it by clicking on the star in your companion's ring menu:
This will open the overview:
Both training points and obedience points make your companion attract more customers. Make sure that his needs are taken care of so that he makes the best possible impression on customers.
Editing your Companion
You can also edit your companion's name and gender in the second tab of your companion overview - for a price.