If you don’t prefer to change the Display name on your Snapchat and opt to have your desired username, then you have you no choice but to deactivate your current Snapchat account (which can only be done from the web version of Snapchat) and create a new account.
Note as well that you can’t transfer account data from the old one. Thus, you can no longer use the deleted Snapchat account username if you’re planning to utilize it in the future when making a new account. So think of these downsides before you decide of having another Snapchat account and username and then deleting the existing one.
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