Just a guess, but I'm thinking the name reffers to a look. You can use this word for spreading sauteed or fried crumbs in butter and then layering them on a dish. So this machine gives the same look.
I found this information in an article related to the history of Welsh Rabbit:
This mystically-named implement was a thick plate of iron attached to a long handle with two feet, or rests, arranged near the heavy end for propping into the heat. Its purpose was to absorb and hold a substantial quantity of heat so that when it was passed, glowing red, over a dish such as Rabbit it would in effect broil it quickly. Its name apparently refers to the small red woodland amphibian which, according to ancient legend, could survive a fire and return to life, phoenix-like. Antique salamanders do not look like the ones used today. The shape of the implement suggests the little creature, its glowing red body, long tail, and feet. Antique salamanders are most elusive today, suggesting that they were not staple cookware in the past.