Missing connector name

If you mean this

it's called a cable lug. You usually don't solder them, but insert the cable/wire and use a crimping tool to fix it to the lug.

They also exist with screw terminals:

or U-shape:

Even tough it may resemble one, this is NOT a banana plug:

• It is a 2.5mm pin plug or 2.5mm male pin connector.
• It is appropriate for low DC (<=60V) or AC (<=30Vrms) voltages and up to a relatively high amount of current, possibly up to 10-15A, depending on the mating subtype and quality of manufacturing.
• It usually comes in two variants:
  • Those where the plug is solid, with no slots, designed to be mated to a pin socket or pin jack with an internal longitudinal spring. Note the spring in the socket is key to ensure the electrical connection.
  • Those where the plug is slotted (like the one in your photo). These are usually mated to a pin socket or pin jack with a precisely machined internal bore, requiring no internal spring in the socket. Here the electrical connection is helped by the two halves of the pin plug, pointing slightly outward, acting as an unreliable spring. If the connection fails, one would usually use a flat type screwdriver "separate" a little bit more the two halves of the pin.
• Note that the two subtypes above are not usually interchangeable: i.e., you will not get a reliable connection between a solid pin plug and a pin socket with no internal spring.

This kind of connector was designed and common use 100+ years ago! It is nowadays a not very common type of connector. Not much cheaper than other similarly cheap connectors and, in fact, much less reliable than those other equally cheap connectors.

I suggest you don't invest too much time looking for a "pin socket to banana plug adapter".

You can easily replace your current pin plugs with a pair of solderable banana plugs. Check also that your laboratory PSU can deliver the amount of current required by the drill.

How to solder a banana plug: https://www.youtube.com/watch?v=Tc0qvbbLL5Q

P.S.: This kind of connectors were mostly employed along with control panels, wiring panels, "plug boards" or training kits, where one had/could manually "rewire, finish or complete the electrical circuit".

As an example, you can find below a "plug board" for an IBM 402 accounting machine.

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Photo taken by Chris Shrigley in May, 2003. Explicit permission granted to upload under Creative Commons licence by Attribution. agr 18:01, 19 January 2006 (UTC).