Well, I believe I should come forward on this one
I myself have been dealing with anxiety and depression for 7years now. I don't find the use of usernames like "DepressedCow" wrong. I think they are perfectly fine. And look I've been through and am going through those feelings myself.
The reason I generally don't have a problem with them is that if that's how people want to express themselves let them. Maybe it's got a more positive message behind the name. Maybe they are spreading awareness? Like if I changed my name to "AnxietyKiller" there's a positive meaning behind it. It's positive due to the fact I want the anxiety killed or to be gone.
I know I'm going to get people disagree with me. But I find you're being quite petty with it. I understand you've been through bad times, so have I with mental health problems. Absolutely horrid things I got so so bad needed a Doctor and all.
You get people who maybe use their sexuality as their username, there are others with their characteristics (hair colour, eye colour) and there are others who use mental health disorders that they have been through. It's part of them, I feel as a believer in this myself you should express your mental health as it can help you find support, it can help you get better.
My look on things like this is names that have Swearing or rude things in them shouldn't be allowed and thats a rule. But I think mental health usernames should be. Although I wouldn't recommend using one as it can be upsetting and it's sometimes misinterpreted
Thanks for taking your time to read, bare in mind this is just my opinion and will probably be with diddly squat to most. So take it how you will