I only stutter on certain letters/sounds. Help?

I only stutter on certain letters/sounds. Help? To start, I work a service job where I go to customers home, and I find it EXTREMELY difficult to introduce myself. My name is Ryley, and it sounds more like I'm uh, uh uh uhhh uhh Rrrrrrrrrr-ryley. And I always get the classic chuckle. It's very frustrating after the 100th time. My parents tell me it's because I'm nervous or being shy, but I really am not. I don't feel nervous at all, in fact I feel very confident in my job and in what I do. Most R words are fine besides my name though. The main one is D works. I could never even think about spitting out a word like Derek, or dissect, or dimple, or anything like that. I can't even get the D sound out and it just sounds like an embarrassing morning/struggling noise. Now don't get me wrong, my stutter isn't too bad. Friends I only occasionally hang out with don't even know I stutter, but sometimes it's bad. It seems like I have my good days and bad days. It's driving me crazy, if anyone has any tips what so ever I'd be so thankful. I am 20, and have been stuttering ever since I can remember. Thank you!