Just saw Jeopardy, where they referenced Israeli currency--shekels. It's the same currency they had 2000 years ago. And Hebrew is the same language they spoke in that land 2000 years ago. They also celebrate the same national holidays that Jesus observed 2000 years ago (like Passover and Hanukkah). Can the so-called Palestinians make the same claim? No, which is why they try to destroy every archeological artifact on the Temple Mount.
Shekels were reinvented when Israel was recreated. Both are modern.
And for the other thing, languages evolve over time, naturally. It may be called Hebrew both now and then but if you could whip up a time machine from one time to the other they'd not likely be mutually intelligible, so it really can't be called "the same language" they spoke then.
No, when languages evolve they are still the same language.
You posted that "the spoke the same language". No language remains static over two thousand years.
Watch this. Or rather, listen to this. Listen to English of one thousand years ago, start at the 3:30 mark to zip right to it.
That's a natural linguistic evolution, and you're talking about twice that long.