It’s unlocked pretty early, too
Here’s how to do it. Note that there are minor location name spoilers: nothing else is spoiled from a story or character perspective.
First, you need to access Roundtable Hold to change your look in Elden Ring. You’ll do this naturally in the story in the very first area, or directly after the first major boss of Stormveil Castle. In any case, you’ll be able to enter it through dialogue via Melina, as you’re resting at a Site of Grace (bonfire). It serves as a sort of NPC and story hub that you can visit anytime by selecting the checkpoint in the lower left-hand corner of the map.
Once you’re there, face the main balcony. Turn right and head through those doors. Then look to the right and go in that room, next to the blacksmith. In that room along the right wall, you’ll find a dressing table and a mirror. Select that you can change your look at will. It’s extremely inconspicuous, and some of you might not even enter the room, so I figured it was worth a tip.
Options include altering your body type, age, and detailed cosmetics, like you were creating your character for the very first time.