According to this Twitter post, her name is 第四号海防艦 (No. 4 Coastal Defense Ship) and she is a Type D escort ship. English-speaking sources seem to use the "CD" prefix to refer to both Type C (odd-numbered) and Type D (even-numbered) escort ships, so I tagged this as cd-4_(kantai_collection).

The Wikipedia article for the ship really is just called 第四号海防艦 and both the Ding class (even) of which she belongs and its companion Hei class (odd) only have their number for a name. Even goroawase is of little help.

FJH said:

The Wikipedia article for the ship really is just called 第四号海防艦 and both the Ding class (even) of which she belongs and its companion Hei class (odd) only have their number for a name. Even goroawase is of little help.

Well, that's basically because she had no actual name - she was a part of mass-produced destroyer escorts, specifically Type-D. It's hard to call her 第四号 (Daiyongo) either - if they just not call her Yon.

Her actions speak more of her that her name though, cause she's stated of sinking both USS Swordfish (SS-193) and USS Scamp (SS-277).

Her self-given nickname is "Yottsu", and I'm generally seeing her 'proper name' being written out as the full "Kaiboukan No.4".

I'm reminded of the running gag in the Starship Troopers movie of the new recruits getting younger and younger.