In Kafka's The Metamorphosis, the boarders might not have names because they are not close to the family—they simply space from a family in dire financial straits that needs money.
More than that, the lodgers may be symbolic representations, so names are unimportant. Specifically, look to the symbolism of Gregor's character. Some sources see Gregor as a Christ-like figure. For example, Gregor works tirelessly for others; and when he cannot live up to the expectations of his family, they reject him. In terms of theology, when the people understood that Christ was not a king that would destroy the Jews' "captors" (the Romans—for that is what they believed the Messiah would do), Jesus was rejected.
There are others examples as well. At one point, Gregor's father throws apples till one lodges in his back: this apple could symbolize original sin (i.e., the Garden of Eden)—and it was for this and all sin that Christ died on the cross. And Gregor, when describing the pain of the apple, notes that he feels "nailed to the spot"—this sounds similar to the way Christ was nailed to the cross:
...[his father] threw apple after apple...One direct hit...penetrated Gregor's back...Gregor...felt like he was nailed down and stretched out...
On the day Gregor dies, there are other instances of Christ-like significance. Similar to the forgiveness that Christ calls down on those who crucify him, Gregor looks at his family the same way—despite his sister's hatred and his father's violence:
He now hardly felt the rotten apple in his back and the inflammation around it, which was now covered in soft dust. He remembered his family with affection and love.
Another religious reference can be seen in the description of his death—note the time when he dies:
Here, Gregor breathes his last. Remembering that the story was not written in English, but in German:
The time of his death, third hour of the morning (German: die dritte Morgenstunde), is not “three o'clock a.m.,” which would be drei Uhr am Morgen in German, and is possibly a reference to the time of Jesus' crucifixion.
When the cleaning women (also nameless), who has been something of a torment to Gregor (perhaps she could represent one of the Roman soldiers that tormented Christ), arrives that morning, she tries to get him to move—and this is how she knows that Gregor has died:
...she tried to tickle Gregor with [the long broom handle] from the doorway. When this also failed to produce results, she was annoyed and poked Gregor gently...
This is similar to when Christ was pierced in the side with a spear. This was done to see what kind of fluids flowed from the wound. Blood would indicate that the heart was still working; anything else would show that he was dead.
In that Gregor is presented as a "Christ-like" figure (with literary allusions to the person of Christ), the lodgers can be seen as more than just tenants, especially because they act as "one:"
The...tenants may be an allusion to the Holy Trinity; the German...literally translates as “room gentlemen.” The German word for gentleman (German: der Herr) means...the same as lord and is used both for other humans and God.
When Gregor is dead (i.e., Christ has died), the lodgers are driven out of the house; as the Trinity, they are rejected as Christ was rejected. Names would be unimportant.