This information could be revealed if you use caller ID and your Google account is configured to allow others to find your profile if they have your phone number.
First, note that even though you're calling through hangouts, caller ID information for your phone can still be sent by Google if you have a Google Voice account or your phone number is verified with Google. From Google's support pages:
Show Google Voice number to call recipients
When you make a call using Hangouts and have a Google Voice number, the recipient will see the call coming from your Google Voice phone number. You can see the phone number that will be shown to recipients when you open the Dialer tab > Dial Pad Dial pad icon.
Show verified phone number to call recipients
If you don't have a Google Voice number, you can turn on Outbound Caller ID on your Android device so your verified phone number shows to the recipient. Your calls from Hangouts will show your verified phone number when you make the calls on your Android or iOS device. When Outbound Caller ID is turned on, you can see the phone number that will be shown to recipients when you open the Dialer tab > Dial Pad Dial pad icon.
So with this feature enabled, people you call will have your phone number. Using that information, the supplier in question may have been able to look up your Google+ profile if you have the "Help people who have your number connect with you across Google services." setting checked on the Phone section of your Google Account Settings page.
Again, from Google's help pages:
You can change your settings to help people who have your phone number find and connect with you on Google services, like Hangouts or Google+.
To use these settings, make sure your My Account "Phone" page shows your current phone number.
Help others connect with you on Google using your number
You can make it easy for people who have your phone number to get in touch with you across Google services. For example, friends can send you a message or photo without having your email address or other contact information.
To help people get in touch by using your phone number, follow these steps:
- Go to the My Account "Phone" page.
- Next to "Help people who have your number connect with you across Google services," check the box.