How to find a specific steam community market user?

There is profile name history, however it can be cleared and then shows "This user has no known aliases".

steamid.uk can sometimes give you historic profile info, but I don't think you can find a profile by a previous name. You would need to suspect a user and look up their account to see if it lists their old name as Cat Ramen.

I originally was gonna suggest backpack.tf to check your inventory history and item history, but 1)I'm not sure how far back bp.tf goes and 2)it appears item history has been wiped couple years ago. You can still try that first tho. Go back to your inventory date of when you still had the hat, click history and check its current owner.
I also did some searching around and found a website(http://www.tf2items.com/) that takes your inventory snapshot periodically(idk how often tho my last one was 2020, then 2019). Clicking on an item will give you the info and more importantly the ID of said item, and then you can append the id after bp.tf history link(https://backpack.tf/item/XXXXXXX for example) to find said item.

Check this link, you can change page and find all your trades, it should be somewhere.
https://steamcommunity.com/id/ViToos/tradehistory/

The trade happened sometime between 2015-04-10 and 2017-01-10, but since you have the confirmation e-mail, you should have the precise date to track the trade down.

You can also try this link, I already put the right filters for you to limit your research, scroll all the way down, load more history, and ctrl+f "ushanka"
https://steamcommunity.com/id/ViToos/inventoryhistory/?app%5B%5D=440&start_time=1484089200

Once you find the trade, and the user, there's a possibility they will have traded the hat away. But maybe you can convince them to follow this same procedure and help you track down the hat. You might be able to use backpack.tf eventually to directly track the item itself eventually.
Let me know if this works, gl!