Great that you got a job that you wanted to do and did not let the stuttering hold you back. I also think that you should tell your co-workers and manager - making jokes about stuttering is not ok. My last job as a software developer we had daily stand ups with the whole group, sometimes remotely also. In the beginning I had really high anxiety about this because I was not comfortable at all plus all those standups was in english ( native swedish speaker ) which was another anxiety speaking another language. But my plan was to just continue to show up and do my best and a couple of months later I felt fine with it - no anxiety. What I did many times was using breathing to calm my body down when the anxiety was high. It was tough at times with lots of ups and downs but I'm glad that I went through that.