A show-off is a fanfarrón. This is a boastful person, or a braggart. It can also be used to describe a loud mouthed or arrogant person.
The feminine form is fanfarrona (without the accent).
The verb form of the word is fanfarronear and means to boast, brag or show off.
[…] Jactarse is to boast or brag. Note that it is reflexive. Therefore it is used like this: “he brags about himself.” Or, “he is a show-off.” […]