The issue is not whether the Jews would call it the holy place, the problem (for your view) is that Jesus
did call it the Holy Place.
Now, if He would've said, "a place the Jews shall call holy", that wouldn't've meant much to the disciples..
15 When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand -
Matt. 24
14 “But when you see the abomination of desolation standing where he ought not to be (let the reader understand), then let those who are in Judea flee to the mountains. 15 Let the one who is on the housetop not go down, nor enter his house, to take anything out, 16 and let the one who is in the field not turn back to take his cloak. 17 And alas for women who are pregnant and for those who are nursing infants in those days! Mark 13
Notice that Jesus is also assuming
legitimacy to the temple He is referring to. "Where he ought not" implies that the person is in a place where he should not be. Now why would God even care about where this (hypothetical) future person should go. After the work of Christ there are
no more holy places (See John 4).
The temple will SEEM legitimate to most of the world. Jesus wanted it to be known where the AOD will occur. And a gentile enterein that temple will be a terrible affront to the Jews. Perhaps God wants it to be profaned on purpose because of the Jews' view of it.
Matthew 24 adds another detail:
19 And woe unto them that are with child, and to them that give suck in those days! 20 But pray ye that your flight be not in the winter, neither on the sabbath day:
Once again, just like there are no holy places, neither are there Sabbath days. That all passed away with the other Commandments of the Decalog.