Sure, people may notice and they're being polite about it. Would you rather they told you something else? I've had a manager with a stutter about 10 years ago. He was an awesome guy. There have also been Presidents with a stutter (Biden), Prime Ministers with a stutter (Churchill), Kings with a stutter (George VI), actors with a stutter (Marilyn Monroe, Bruce Willis, Emily Blunt, Rowan Atkinson), singers with a stutter (Elvis Presley, Ed Sheeran, Kendrick Lamar) and many more. You have a stutter. It sucks. You also have a good job and you'll make the best of it, I'm sure. I'm rooting for you and hope that one day people will add your name to their lists of people who inspire them. Go be your best self and don't let anyone get to you.