The New Testament
Who was the priest?

And he said to them, “Have you never read what David did, when he was in need and was hungry, he and those who were with him: how he entered the house of God, in the time of Abiathar the high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and also gave it to those who were with him?”” (Mark 2:25–26)

The apparent confusion is already evident in Tanakh.

1 Samuel 22:20
"But one son of Ahimelech the son of Ahitub, named Abiathar, escaped and fled after David."
Ahitub → Ahimelech → Abiathar.
2 Samuel 8:17
"Zadok the son of Ahitub and Ahimelech the son of Abiathar were priests."
Abiathar → Ahimelech
Ahitub → Zadok
1 Chronicles 18:16
"and Zadok the son of Ahitub and Abimelech the son of Abiathar were priests..."
Abiathar → Abimelech
Ahitub → Zadok
1 Chronicles 24:3
"...Zadok of the sons of Eleazar and Ahimelech of the sons of Ithamar..."
Ithamar → Ahimelech
Eleazar → Zadok
1 Chronicles 24:6
"...Zadok the priest, Ahimelech the son of Abiathar..."
Abiathar → Ahimelech
So pulling this all together what do we have?
Ahitub → Ahimelech → Abiathar → Ahimelech.
But Abiathar was the dominant character and associated strongly with David. It's interesting that in Tanakh Ahimelech is not called 'high priest', just the priest and other priests are mentioned. Also, if both Abiathar's father and son are called Ahimelech, without the text telling us, how do we know who was high priest? Furthermore, it is quite common when referring in the past to a later titled person. For instance when looking back to WW2 one could say '...the Queen did...' She's queen now but George was the monarch then. So Mark could be referring back to the days of Abiathar, even before he became high priest. After all, Abiathar is the only one who came out of that incident unscathed.
The New Testament - A Roman Invention?
Some say that Jesus is a Roman myth and that his name means 'hail Zeus'.

χαλαζι ζευς = Chaladzi Zeus

Ιησους = Iesous

There is no correlation between the phrase χαλαζι ζευς (hail Zeus) and the name Ιησους.

In the NT book of Hebrews it says concerning Joshua: “For if Joshua had given them rest, He would not have spoken of another day after that.” (Hebrews 4:8). In Greek the name Joshua is Ιησους. In the Tanakh Joshua is יְהוֹשׁוּעַ and occurs 218 times and 28 times as יֵשׁוּעַ. The Greek version of the Tanakh translates these names as Ιησους. Philo tells us that Ιησους is a contracted translation of יה שוע Yah Shu'a (Yah saves) in Mut 1:121: " Ἰησοῦς... σωτηρία κυρίου - Iesous... salvation of the Lord."
When referring to his name, Matthews writes: "She (Mary) will bear a son, and you shall call his name Ιησους, for he will save his people from their sins." (Matthew 1:21).

In spite of the vain search for a Roman origin the story is a Jewish story with a Jewish main character with a Jewish name. The Tanakh agrees, The Jewish writers Josephus and Philo agree and the NT asserts it.

The Aramaic Peshitta translates from the Greek
“ܬ݁ܺܐܠܰܕ݂ ܕ݁ܶܝܢ ܒ݁ܪܳܐ ܘܬ݂ܶܩܪܶܐ ܫܡܶܗ ◄ ܝܶܫܽܘܥ► ܗܽܘ ܓ݁ܶܝܪ ܢܰܚܶܝܘܗ̱ܝ ܠܥܰܡܶܗ ܡܶܢ ܚܛܳܗܰܝܗܽܘ̈ܢ”
(Matthew 1:21)

So in the Aramaic communities of the East Ιησους was translated into ܝܶܫܽܘܥ which in Hebrew script is יֵשׁוּעַ (Yeshua). So there is overwhelming evidence that Ιησους is from the Hebrew יֵשׁוּעַ and not some Greek pagan phrase.