interruption in speech

How can I insert saying someone’s name in a sentence without the sentence being addressed to them.

For example, I am talking to myself, "I have to go to the bank and the dry cleaners today, June (I call out the name of my puppy who is scratching my furniture in hopes that he will listen and stop), after I have lunch."

If I write it as is, with commas and all, it sounds as if I am saying the entire sentence to June, when, in fact, I am talking to myself. Is it possible to call out a person’s name in the middle of a dialogue or conversation without having the previous spoken dialogue addressed to that person?