Ha'aretz explains how the Jewish state came to be called "Israel," something I've wondered about. I still think "Judea" or "Zion" would have been a better name. Ever (state of the Hebrews) was among the other names considered.
The objection that "Judea" was an actual historic state, much of whose territory was not included in 1948 Israel, neglects the fact that there was also a historical Kingdom of Israel, whose territory was also not included in 1948 Israel (Har Gerizim, for example, the site of the Israelite temple, is in Samaria, part of West Bank). Moreover, it would have made a pertinent political point to call the country "Judea"--that the 3rd Jewish commonwealth need not occupy the exact same territory as its predecessors, a point that some of the Messianic elements within the Israeli Jewish community would do well to heed.