I'm very perplexed at this passage. I haven't read Shogun, but I looked up the passage which runs as follows:

"Ah yes! He's Akabo. But that just means 'porter,' senor. They don't have names. Only samurai have names."

"What?"

"Only samurai have names, first names and surnames. It's their law, senor. Everyone else has to make do with what they are - porter, fisherman, cook, executioner, farmer, and so on. Sons and daughters are mostly just First Daughter, Second Daughter, First Son, and so on. Sometimes they'd call a man 'fisherman who lives near the elm tree' or 'fisherman with bad eyes.' " The monk shrugged and stifled a yawn. "Ordinary Japanese aren't allowed names. Whores give themselves names like Carp or Moon or Petal or Eel or Star. It's strange, senor, but it's their law. We give them Christian names, real names, when we baptize them, bringing them salvation and the word of God..." His words trailed off and he slept.

Hideyoshi restricted the use of surnames to samurai at this time, so the remark about samurai surnames makes sense, even if it flew in the face of previous traditions, and was often ignored in practice. But the idea that every other person had no personal names is really bizarre. Is the priest here meant to be exaggerating? For instance, does he not register ordinary Japanese given names and nicknames as "real names"? Names by position in the family "Ichiro" (First son) etc. were indeed pretty common.

This priest also doesn't seem to be aware of the imina: the personal name that would probably fit his definition of a "real name." The imina, often called the posthumous name, or taboo/secret name in English, was a personal name that usually wasn't used by the person in life, and in some periods was a family secret, but they'd be identified by that name after death. (The rationale for hiding the imina seems to be related to the longstanding belief that to know someone's true name is to have power over them.)

The official prohibition of surnames to non-samurai did have a consequence in modern times, though. It led to a huge variety of Japanese surnames when in the late 19th century, everyone was required to register a surname. For details on that, check my answer Are there particular historical factors (e.g., clans, castes, culture), that led to Japan having a much wider variety and complexity of surnames than the rest of the Sinosphere?