I wonder if they considered simply using what was the most common name for the region at the time, and call the newly-independent Jewish state the "Republic of Palestine".
Hebrew and Yiddish literature almost never used the term Palestine, using Land of Israel basically exclusively. Going back continuously since the Second Diaspora.
In English and German, Zionists did often refer to the region as Palestine (though also as "Eretz Yisrael" - "Land of Israel" in Hebrew). A lot of earlier Zionist literature does use the term Palestine (for example, Auto-Emancipation and Altneuland).
But by the time of the establishment of the state, the language of the Zionist shadow government was Hebrew. Plus, the Mandate of Palestine was being split to establish two state, and it was presumed that the Arab state would call itself Palestine.
If they had called the state Judea or some variant it would, at the time, have contained little if anything of Judea.
Meh; not sure how relevant, though I have always found it a little ironic that modern Israel does not contain the heartland of ancient Israel (the Judean Hills, which is more or less geographically the same as the West Bank)
Calling the state "Palestine" would have implied a claim on the East Bank.
Ancient Israel also included land on the east bank of the Jordan, which not including most of the Negev, and a large portion of what is now the coast of Israel, both to the north (where it was controlled by Phoenicians) and the south (Philistines).
Some Zionist factions pushed for the entire Mandate (including what would become Transjordan), some for anything they could get (the Peel Commission plan had a good amount of support, and would have made a Jewish state in the Galilee plus a narrow strip along the coast, with the rest being Arab except for an international corridor from Jerusalem to Jaffa)