Does anyone know the name or have a link to an electrical testing device for verifying home-runs to electrical box?
If you are trying to label or find a wire, the typical way is to use a wire tracer. One end is a tone generator, the other end is a detector that can hear those tones.
You can get low-voltage ones, which can be used for (unpowered) electrical cables, ethernet/phone and cable:
You can also get specialty live-voltage tracers, many of which can be used if the circuit is powered:
If you're actually trying to get continuity (and get an ohms value) one way is to use a standard multimeter with a long extension cord. This only works if the circuit is unpowered (otherwise you risk blowing up your meter and/or electrocuting yourself). Plug in the extension cord at one end, and bring the other end to the source (eg, near the panel), then you can use one of the multimeter probes on the extension cord and the other on the wire you're testing.