How did the writers not notice that the mailbox of Leela's parents says "Turanga," and not "Leela"?
Turanga Leela is Leela's proper name, with Leela being her surname, so shouldn't it follow that her folks would be the same?
How did the writers not notice that the mailbox of Leela's parents says "Turanga," and not "Leela"?
Turanga Leela is Leela's proper name, with Leela being her surname, so shouldn't it follow that her folks would be the same?
Turanga is the family name. Her parents names are Turanga Morris and Turanga Munda.

In certain cultures, a surname (i.e. family name) is said first when pronouncing a person's name. Leela's family appears to follow the same tradition, with "Turanga" being their surname, not "Leela". This is why it (intentionally) appears on the mailbox of their sewer home.
Although transcripts for episodes sometimes refer to Leela's parents by their full names (Turanga Morris and Turanga Munda, listing "Turanga" as the common first surname), I don't believe their full names are ever explicitly said aloud as Leela's name often is (such as in the season 4 episode Leela's Homeworld, when she is receiving her "Orphan of the Year" award). The closest I found was from the season 7 episode Zapp Dingbat, when Zapp (who is dating Leela's mother) refers to Leela as "my second favorite Turanga girl".
The pronunciation of the surname first suggests they may be of Hungarian or East Asian descent, although this is never established or referenced in the show. Since "Leela" sounds like the word for "purple" (her hair color) in Hungarian ("lila"), then Hungarian (speculatively) seems like the most likely lineage for her family.
The writer's did notice. Putting the name "Turanga" on the mailbox was an intentional move. Everybody puts their family name on their mailbox and the Turanga family are no exception.
In the episodes Leela's Homeworld, Teenage Mutant Leela's Hurdles, Less than Hero, Bender's Big Score, Bender's Game, The Mutants are Revolting, Mobius Dick and Zapp Dingbat her parents make appearances. Countless times, in many of those episodes, if not all, their names are spoken aloud as Turanaga Morris and Turanga Munda providing evidence that Turanga--being common to all of them--is their family name (also known as a surname).
Putting the name "Turanga" on the mailbox only helps to drive this fact home.
If you'd like to know why their names are reversed, I posted a related but different question over here.