In a binangle hatchet push excavator, hatchet denotes the:
G.V. Black described a way to name dental instruments which is similar to zoological classification:

The order denotes the purpose of the instrument, e.g., excavator, scaler.
The suborder denotes the position or manner of use of the instrument, e.g., push, pull.
The class describes the form of the blade, e.g., hatchet, chisel.
The angle denotes the number of angles in the shank. If the instrument contains one angle in its shank, it is called monangle. If it contains two angles, it is called binangle. If it contains three angles, it is called triple-angle. Four angles are called quaternary-angle.
Naming of the instruments usually moves from 4 to 1.

For example, a binangle hatchet push excavator. In most cases, the suborder describing the position or manner of use is variable and non-specific, and for practical purposes, it is usually omitted. Identifying the working end and the purpose of the instrument is sufficient, e.g., binangle hatchet excavator.
Ref: Sturdevant's art and science of operative dentistry. 4th edition page 309
Operative dentistry modern theory and practice Marzouk page 59
Class
Subclass
Order
Suborder