Many moons ago I had a neighbor that had a Llama. I do not recall it's name. It used to follow people around, too. Had a weird habit of tapping people on the shoulder with its face to get attention. Loved to be pet, but was a little nervous around the wee ones. I think she was afraid of hurting them.
Not sure why your story reminded me of that, but here we are
As long as the llama doesn't go for the reach around!