"Is this how you talk to customers?"

"Is this how you talk to customers?" I work in customer services. Every time when I picked up a call, I could only say "hi". I wanted to say more, like "thanks for calling ..." or "this is ..., how can I help you?", but stuttered so bad on "thanks" and "this" that I couldn't even start the sentence. Today a lady called in. I said "hi" then stayed silent, waiting for her to respond. She asked, "is this how you guys talk to customers?" I felt so bad and explained to her that I was "new" and not "familiar" with the job. I did start the job not long ago, but the reason I stayed silent was because of my stuttering. I don't know how long I had to use "I'm new" as an excuse. Just tired.