My stutter is a lot worse and to the point that i can speak 1 word in 5+ secs on a good day. I graduated last year as a software engineer as well and faced this issue a lot. In one interview, the interviewer asked for my intro and before i could say my name, he stopped me and told me to send the nezt guy in on the way out. Had a couple other rejections as well. Probably one of the worst times in my life when i had to find a job. I did get one later where I'm working right now. They allow me to write what i have to say in chat for now. Going good for now but not sure about the future. Good luck for your future interviews.