In real life when a player gets a red card after receiving a yelling, what happens...

does the ref show the yellow then red and then write the name in the books

or

does the ref write his name in the book and then show him the card

or

is it always different depending on the ref?

The ref is supposed to write the number of the player involved in any transgression before penalising the player.
Should a card be required, then this is shown after writing down the player's number.