I think it would be helpful to have a semi-automated tool. I see the technical challenges with making one (yes, the words "denormalized text field" mean something to me), but I think it's more than possible to make one that's good enough. I imagine a tool where a moderator (on the request of a user) would input the user's ID and their (old or soon to be old) display name, and get a list of comments that refer to the display name, using the same algorithm that shows you what's in your inbox (all comments on your posts and also comments containing @name; maybe in the case of a more unique name all comments should be searched). The moderator would then have to select one of several options for each: skip (leaves the comment alone, used if it's a false positive), edit (replaces the old name with a new name), or delete.
But nothing like this exists right now. The option that's most convenient — for moderators at least — is probably yes, for you to compile a list and start flagging those comments after first explaining your situation. You should flag from your main account, the one the comments were addressed to. (You likely don't have enough flags to do this in one day, though.)
However, I suspect needing to do that will be distressing to some, so if you have this problem on the site where I moderate (Writing), you can drop a single "in need of moderator attention" flag explaining your situation and we'll see about helping you. (PS I hope you are working to get through your feelings so you can feel better soon.)
If you can hold off on changing your name, then a moderator can find comments addressed to you using your site inbox, which is found in your profile, under "activity" then "responses". Otherwise, it's possible to use SEDE to find the comments, including some missed in your profile. I found this very basic query which sometimes works well, sometimes doesn't. The information there is only updated on Sundays. (If there's too much noise, then the query would have to be edited to be restricted to only certain comments, maybe by filtering based off a list of parent posts that you were involved in: posts you made or have visible comments on. However, I'm not sure if it would time out, like even the basic query did for me on Stack Overflow.)