Historically, a "Christian" (Christianus) was someone who
worshipped Christus "as a god". (Ref.: Pliny the Younger)
According to the Pauline teaching, there is "ONE GOD" and
"ONE LORD", so, apparently they also worshipped a deity
under the name of THEOS or DEUS, who was none other than
ZEUS/JUPITER, father of the "Lord Christus", since Christus
took the place of the Hebrew YHWH or ADONAI ("Lord") as the
creator of this world.
Later the Church added yet another deity, the "Holy Ghost/Spirit"
to make their god into a Trinity.
Jews and Muslims are not permitted to worship any deity
other than YHWH or ALLAH, so there can be no Muslim of
Jewish "Christians".

As for the "King of the Jews", the last king of the Jews was Herod
Agrippa, who ruled between 10 BCE and 44 CE. He was the grandson of
Herod the Great, and son of Aristobulus IV and Berenice. His original
name was Marcus Julius Agrippa.

There was no king of the Jews named "Jesus" or Iesous.