This topic deserves much more time and space than I can give it.
Christus (Greek Christos) or Chrestus (Greek Chrestos) that is the question, and an important one. Most anyone doing research on Christian origins has encountered the use of the word "Chrestus", often wrongly equated with Christ in dictionary and commentary. For instance the infamous Suetonius reference to a rebellion in Rome that needed to be squelched. Quote: "drove the Jews out of Rome, who at the suggestion of Chrestus (Latin for Chrestos) were constantly rioting." is often hailed as proof of the existance of an historical Jesus. The obvious problems with identifying this person with Jesus (Jesus not in Rome and Christains starting riots?) with this conclusion aside we have to ask what the word 'Chrestus' meant. Rather than being a simple misspelling of Christus, "Chrestus" was a comon name found in over 80 inscriptions meaning "good, sweet, useful". It was often used in reference to slaves that had earned freedom. It also however had a long standing religious use as name of divine agents and deities such as Mithra, Apollo and Serapis. This last point is significant. To those that perceive earliest Christain origins from the pagan Mysteries it seems quite expected that the earliest references to the faiths leader us the name Chrestus as it was in use by similar cults. To those who feel Jewish messianism was the home soil of the new faith then the form Christos (word coined as rough equivilant of Hebrew Messiah) would be assumed the original with Chrestus being a corruption. Interstingly Gnostic Christains felt the two terms were grades of initiation, the newbie convert called Chrestus until reaching full intiation and annointing then called Christus. They (broad brush) felt Jesus was not the only Christus but all could attain to this Christus state. ( Makes me think of Paul.) The actual NT is of little help as the titles and names of God and Christ have been reduced to abbreviations in the tradition of the Nomina Sacra.
Below I will list some of the usages of these and related words (other than the references to pagan deities):
Sibylline book, the Erythrean, contains an acrostic in Greek, now extant, the initial letters of which are--
....[six Greek words]* ["*Iesous Chreistos, Theou Uios, Soter, Stauros. Jesus Chreist, God's Son, Savior, Stake."
Note: the spelling Chreistos may reflect older from of Chrestos The most ancient dated Christian inscription (Oct. 1, 318 A.D.) on Marcionite church runs "The Lord and Saviour Jesus the Good (Chrestus)"
Clement of Alexandria said, "all who believe in Christ are called Chrestoi, that is 'good men."
Hadrian wrote, "There are there (in Egypt) Christians who worship Serapis; and devoted to Serapis, are those who call themselves 'Bishops of Christ'."
Note: I included this because it may reveal a relataionship
Theophilus of Antioch (A.D. 168-188) puns upon the name Christian. "I, for my part," says he, (B. i, ch. 1,) "avow that I am a Christian, and bear this name beloved of God, hoping to be serviceable, (euchrestos.)" In ch. 12 this punning is kept up throughout, thus:
"And about your laughing at me, calling me 'Christian,' you know not what you are saying. First, because that which is anointed is sweet (Chrestos) and serviceable, (euchrestos,) and far from contemptible......And what work has either ornament or beauty unless it be anointed or burnished? Then the air and all that is under heaven is in a certain sort anointed by light and spirit, and are you unwilling to be anointed with the oil of God? Wherefore we are called Christians on this account because we are anointed with the oil of God."
Note: here Theo (if not altered) is addressing the issue of the names by finding value in both, also identies himself as Christian because he was annointed not because of being follower of a Christ. Similar to Gnostics as noted above.
Lactantius, (A.D. 301-330,) who wrote in Latin said the Greeks "were accustomed, through a mistake of ignorance (?) by the change of a letter, to say Chrestus." (Div. Inst., B. iv, ch. 7.)
Here a Latin speaking writer suggests the Greeks had confused the Greek word.
Tertullian (A.D. 193-220) also Latin speaking, says:
"But Christian, so far as the meaning of the word is concerned, is derived from anointing. Yes, and even when it is wrongly pronounced by you Chrestianus, (for you do not even know accurately the name you hate,) it comes from sweetness and benignity." (Apol., Sec. 3. See also Ad. Nat., ch. 3.)
Note: again Latin writer blaming Greeks for mispronouncing a Greek word, also note Christian is referring to their annointing not to a Christ follower. Both Tertullian and Lactantiuselsewhere said the common people usually called Christ Chrestos.
Here an example that show evidence of altering the name from "e" to "i":
Justin Martyr [c. 100 - c. 165]"First Apology," ch. 4, this passage occurs:
"So far, at least, as one may judge from the name we are accused of, we are most excellent (crestotatoi) people......For we are accused of being Christians, and to hate what is excellent (chrestos) is unjust."
Here the in word Christianoi the e has evidently been changed to i, for the sentence certainly requires Chestianoi for the argument to flow.
Here's an interesting verse that has been altered, apparently at the time when the transformation from Chrestus to Christus was being made.
In 1 Pet., ii, 3, we read, "If so be ye have tasted that the Lord is good (chrestos.)" Some manuscripts have christos, an evident corruption. " The passage is evidently taken from Ps. xxxiv, 8, which reads, "O taste and see that the Lord is good"--chrestos in the Septuagint.
This raises questions about passages like Phil. i, 21, "For me to live is Christ, and to die is gain," the parallelism seeming to require Christ here mean Chestos to correspond to kerdos, "gain."