Use Cases
Aesthetic Instagram Names
Display-name styles that survive Instagram's field rules.
Short answer
Style the display name, leave the username plain. Instagram accepts styled characters in the name field but validates the handle, and a plain handle is what keeps you findable and taggable.
Name versus username
Instagram's display name accepts styled characters; the username does not. Style the name field and leave the handle plain so people can still find and tag you.
Why the two fields behave differently
Instagram's display name is descriptive; the username is an identifier that appears in your profile URL and in every mention of you. Identifiers have to be unambiguous, so the username field validates against a restricted character set while the name field does not. This is a deliberate design decision rather than an oversight, and it is consistent across most platforms.
What you lose if you style the handle anyway
You cannot, on Instagram — the field rejects it. On platforms that do allow it, the cost is that people cannot type your handle from memory, autocomplete stops finding you, and anyone trying to tag you has to copy and paste. For an account that wants to be found, that is a steep price for a visual effect.