The meta answer is MARIO (Hint: Find a 5-letter first name.)
In this puzzle, the longest answers aren't where to look for the hint. Instead, you perhaps noticed that five symmetrically placed Across clues, all the middle words of their respective rows, are plumbing tools--even though they weren't clued as such. (The words are SNAKE, BENDER, PLUNGER, WRENCH, and GAUGE.)
You might have made the leap at this point from "plumbing tools" to "MARIO" based on the hint alone, but in case you didn't, the puzzle's title, "Extra Parts Included," provided another hint. In each row where there's a plumbing-related word, the two words before and after each plumbing term form an anagram of that plumbing word--plus an extra letter (or "part") that's "included" in each surrounding pair of words:
ASK + MEN = SNAKE + M
BARE + DEN = BENDER + A
PURR + GLEN = PLUNGER + R
NEW + RICH = WRENCH + I
AUG + EGO = GAUGE + O
From top to bottom, those extra letters spell MARIO, arguably the world's most famous fictional plumber and a 5-letter first name that satisfies the puzzle's hint.