Using platforms such as Google Analytics to check your engagement metrics, or to create goals alongside Google Tag Manager and see if people have converted, are helpful (free) tools to use.
Don’t forget to monitor your social media accounts for post engagement, as well as diving into online brand communities to see what people are saying about you.
There are offline ways to audit your brand, too.
Research methods such as focus groups and interviews can help you test different elements of your brand awareness.