What is the name of a footprint that is designed to let you cut the trace between two nets?

Sometimes called a "Solder-Short" pattern. To create it you could use two half-moon shaped pads placed very close together, be sure to keep solder mask off the junction area. Usually the idea here is if you need the two signals shorted you then put down a solder blob covering both pad ends. With this method you start out with an open.

A way to create it and still keep the net connection would be to use an oval shaped pad with an oversized (non-plated) drill hole. You then run the two traces to the pad from opposite ends. The drilling of the over-sized hole physically cuts the pad in two. Re-solder the connection if needed later on.

In Sparkfun-Passives Eagle library the part is called JUMPER-PAD, with several variants, like -NC (normally closed, i.e., paste layer present over the jumper), -NO, as well as one with a copper trace shorting two halves. Both 2 and 3 way, 3 way with paste or trace over 1,2 or 2,3.

Maybe you want to use a solder short and parallel it with a single-layer pad that can be drilled out. You'd probably want to make the drill-out pad and connections to it a net tie so the DRC deals appropriately with the shorted connections to the solder short. Here (from an earlier post of mine) is the solder short portion: