How we cite our quotes:
Quote #4
CASTIZA
Tell him my honour shall have a rich name,
When several harlots shall share his with shame.(2.41-42)
It's not just about external reputation for Castiza—it's also about honor, a quality she carries within herself, which we see here when she speaks to Lussurioso's messenger. Honor is linked to reputation (she definitely doesn't want to have her name sullied by accepting Lussurioso's offer), but it's more than just external. Incidentally, she majorly disses Lussurioso here by implying that his reputation is going downhill fast.
Quote #5
VINDICE
Oh I'm above my tongue! Most constant sister,
In this thou hast right honourable shown;
Many are called by their honour that have none,
Thou art approved forever in my thoughts.
It is not in the power of words to taint thee.(2.1.49-53)
For a man just slapped by his sister, Vindice's awfully happy. Along the way, he shows that he also thinks honor and reputation aren't quite the same (though they might overlap), and here he's glad Castiza seems to have both.
Quote #6
VINDICE
So may you, lady.
One that is like to be our sudden duke,
The crown gapes for him every tide, and then
Commander o'er us all: do but think on him.
How blest were they now that could pleasure him
E'en with anything, almost.
Mother. Ay, save their honour.(2.1.65-71)
Vindice's mother may cave later to encouraging her daughter to sleep with Lussurioso for money, but she starts off this conversation by asserting the importance of honor. Is this one reason she repents later in the play—because she actually cares about honor deep down?