T'hillim / Psalm 2:6: says “I Myself (G-d) have anointed My king (King David) over Zion (the land of Israel), My Holy Mountain!” Is this a prophecy that Jesus will "own the title King"?
T'hillim / Psalm 2 is not a prohecy, it is a poem / prayer written by King David and he is speaking of himself as a king -- it has nothing whatsoever to do with Jesus (who was never a king, so the claim is false that Jesus "owned the title of king").
Read the first few lines of the psalm:
"Why have nations gathered and [why do] kingdoms think vain things? Kings of a land stand up, and nobles take counsel together against the L-rd and against His anointed (messiah)? "Let us break their bands and cast off their cords from us." He Who dwells in Heaven laughs; the L-rd mocks them. Then He speaks to them in His wrath; and He frightens them with His sore displeasure. "But I have enthroned My king on Zion, My holy mount." T'hillim / Psalm 2:1-6
Reading those first five lines it is easy to see they do not apply to Jesus, but they do apply to King David.
Missionaries will often say that Jesus was the last possible Jew to be the messiah (some say the geneaologies were kept in the Temple and destroyed when the Temple was destroyed). These are lies. There are men alive today who can trace themselves to Kings David and Solomon. Others may say that the bible says that it has been "too long" since the last Davidic king and that the bible said the Davidic throne would never be "empty." If this were true (and it is not) then they just eliminated Jesus from the throne as well since 600 years lapsed between the last Davidic king and the time of Jesus. . .
Quite simply, Jesus was never a king, and he did not have the right to be a king. This is yet another claim made that is easily disproved by simply reading the T'nach (Jewish bible).