The name of the Parshah, "Tetzaveh," means "Command" and it is found in Exodus 27:20.
G‑d tells Moses to receive from the children of Israel pure olive oil to feed the “everlasting flame” of the menorah, which Aaron is to kindle each day, “from evening till morning.”
The priestly garments, to be worn by the kohanim (priests) while serving in the Sanctuary, are described. All kohanim wore: 1) the ketonet—a full-length linen tunic; 2) michnasayim—linen breeches; 3) mitznefet or migba’at—a linen turban; 4) avnet—a long sash wound above the waist.
In addition, the kohen gadol (high priest) wore: 5) the efod—an apron-like garment made of blue-, purple- and red-dyed wool, linen and gold thread; 6) the choshen—a breastplate containing twelve precious stones inscribed with the names of the twelve tribes of Israel; 7) the me’il—a cloak of blue wool, with gold bells and decorative pomegranates on its hem; 8) the tzitz—a golden plate worn on the forehead, bearing the inscription “Holy to G‑d.”
Tetzaveh also includes G‑d’s detailed instructions for the seven-day initiation of Aaron and his four sons—Nadav, Avihu, Elazar and Itamar—into the priesthood, and for the making of the golden altar, on which the ketoret (incense) was burned.
Learn: Tetzaveh in Depth
Browse: Tetzaveh Parshah Columnists
Prep: Devar Torah Q&A for Tetzaveh
Read: Haftarah in a Nutshell
Play: Tetzaveh Parshah Quiz
How did the other Israelites know that someone was a priest if he did not wear priestly clothing outside the Sanctuary, without asking his last name?
And how many men with the surname Cohen are actually Cohen nowadays, considering that there are many mixed marriages between Jews and non-Jews?
Families had tradition of being Kohanim, and these traditions were known within the community.
Today, a surname is not much of an indication, including for people with two Jewish parents, since many people adopted names from other families.