A name, or their face
A name changes the line. A face puts them in the picture. Those are not the same weight.
The name is a finger
Put a name in the line when the joke was waiting for someone. "You" is a crowd. Their name points. The same picture becomes about them, and only them.
If the joke still works after you delete the name, you did not need it. A name that is only decoration feels like a mail merge. Say it, or type it, only when the line was empty without them.
The face is heavier
A face puts them in the picture, not in the caption. That is funny when the picture is already the situation they are in. It is a hit when the picture is a humiliation they did not agree to stand in.
Use a photo you are allowed to use. One they sent you. One from the night. One already in the chat. Not a picture you saved off someone else's story.
When you are unsure
Use the name. A name can be shrugged off. A face sticks to the joke. Save the face for the person who would have put themselves there.
The photo stays in the browser you used. It is not an account, and it is not a pack you keep for later. If you would not want that face kept, do not upload it.