From EnquiryBot you can email customers in 2 ways.
By replying to enquiries right from within your inbox
When you setup custom autoresponders for your bot enquiries
In both these cases you can send emails from your username and add your own email signature to those emails.
Creating your email signature is easy.
Step 1. Go to the top right of the screen and click on your user icon. Then select "Profile"
Step 2. Click on the " + Signature " button
Step 3. Add your signature in the box and save