Well, first of all, the original version of this—and this Steam release—never actually shows the tool Rena is carrying, and simply describes an "axe" (斧 "ono"). Incidentally, you can look at the Japanese text. From in-game, you can go to the menu and switch it, or just press "L". The scripts (code the engine reads to determine what to show when) are also available in
(game folder)/HigurashiEp##_Data/StreamingAssets/Scripts
where ## is the number according to Steam release.

As for how the anime depicts it, I've seen it called a "billhook". Searching for "japanese billhook", I find the words "nata" and "kama". It looks like some have a projecting part at the end that looks a bit like the hook on anime Rena's tool.

offically called a nata