Luke 8:3 says that Joanna was the wife of Chuza Herod’s "epitropos". Another text may shed further light on this. In John 4:46ff we read that:
46 So he [Jesus] came again to Cana in Galilee, where he had made the water wine. And at Capernaum there was an official basilikos whose son was ill. 47When this man heard that Jesus had come from Judea to Galilee, he went to him and asked him to come down and heal his son, for he was at the point of death ...
50Jesus said to him, “Go; your son will live.”
The man believed the word that Jesus spoke to him and went on his way. 51As he was going down, his servants met him and told him that his son was recovering. 52So he asked them the hour when he began to get better, and they said to him, “Yesterday at the seventh hour the fever left him.” 53The father knew that was the hour when Jesus had said to him, “Your son will live.” And he himself believed, and all his household. 54This was now the second sign that Jesus did when he had come from Judea to Galilee.
There are a few parallels in this text with the account of the healing of the centurion’s servant, which was also in Capernaum (see Matthew 8:5ff, Luke 7:1ff), but there are also some important differences. Matthew and Luke report that the person healed was the centurion’s paralyzed slave, whereas John 4 indicates that it was the official’s dying son. Furthermore, the man of John 4 was a “basilikos”, or royal official of king Herod, while a centurion would have been a Roman officer. A search for the word "basilikos" among the ancient Greek works in the Loeb Classical library led to the following renderings of this term: “a nobleman”, “an aristocrat”, and “a man of the royal court”. Literally, the word could be translated, "little king".
In 1874, F.W. Farrar commented on this passage saying:
As this courtier believed in Christ with his whole house, in consequence of the miracle now wrought, it has been conjectured with some probability that it was none other than Chuza himself (Lk 8:2-3)… The position of the courtier caused it to be widely known, and it contributed, no doubt, to that joyous and enthusiastic welcome which our Lord received during that bright early period of his ministry.
-- The Life of Christ (vol. 1, p. 230-232).
If Farrar is correct that Joanna's husband Chuza was the royal official of John 4, this would make a great deal of sense, since we're told that he, along with his entire household, believed. This would explain why a woman of Joanna’s noble status would later be found following Jesus around Galilee and Judea, and supporting him financially, and it may also explain the faith of Herod's foster-brother Manaen, who according to Acts 13:1 was found to be one of the earliest leaders of the church in Antioch around 45 AD.
Finally, the word "epitropos", used in Luke 8:3, fits beautifully with the word "basilikos" that we find in John 4:46. One is a royal official, or nobleman, while the other is specifically identified as Herod’s governor, administrator, or prime minister. Strabo uses the word "epitropos" to describe “Sylleus the administrator of king Obodas of Nabatea”.
According to one historian:
Obodas confirmed Sylleus as chief minister and almost immediately, Sylleus initiated negotiations with both the Romans and Herod the Great… Some think Sylleus was setting himself up to be the next king.
Josephus also notes that:
There was one Obodas, king of Arabia… but Sylleus administered most of his affairs for him.
-- Antiquities of the Jews (16.7.6).
The word he used here (translated administered) was "dioikeo," which is a synonym of the word epitropos. Chuza, therefore should be seen as Herod’s chief administrator, or even better, his "prime minister," rather than a mere "household manager” (as per the ESV).
So if the basilikos of John 4:46 is Chuza, why doesn't the author of the Fourth Gospel identify him by name? My guess is this has something to do with "protective anonymity", which is an idea that Richard Bauckham and Gerd Theissen mention in their writings. John relates this royal official's story in an anonymous way since it was written during a time of persecution and so the author was "protecting his source".