When you get nitro, you have the ability to customize your tag. When your nitro expires, your tag gets randomized. Your name and your tag are used to identify you in discord, so when it randomizes, you either have to update your tag on all the places you've shared your discord on, or have people not be able to find you. Quite a few times I have gone to contact someone for a commission, and the tag they shared didn't work because they forgot to update the tag after nitro expired.
TL:DR: your discord name/tag should be reliable, and not change when you don't want it to.