A black lamp works in almost any room that already has some warmth in it, wood tones, a rug with pattern, a wall color that isn't stark white. It pulls focus in a way a white or ceramic lamp never does, which is exactly the point, but if your room is already dark or short on windows, think twice before putting a black base on a black side table against a dark wall. You will lose the shape of it entirely. In a bright room, or sitting on a pale surface, that same lamp looks sharp instead of swallowed.
When you're looking at one in a shop or unboxing it the day it arrives, check the base is actually heavy. A lot of cheaper black lamps are light as a shoebox and tip the second a cord gets tugged, which matters more with a dark finish because every little wobble and scuff shows up against black in a way it wouldn't on a cream lamp. Run a hand over the finish too. Some are a flat, slightly rubbery matte that picks up fingerprints and dust in a way that drives you up the wall, others are a harder satin black that wipes clean with a damp cloth and stays looking sharp. Check the switch is in a sensible spot, not jammed under the shade where you're patting around in the dark every night.
Good ones age well. The finish on a solid metal or ceramic black lamp doesn't fade or go patchy, it just needs a wipe down now and then and the odd polish with a dry cloth to keep the sheen even. Cheap ones are the opposite story, the paint or coating can chip at the base or along the neck within a year, and once black paint chips it shows white or silver underneath, which looks worse than almost any other color doing the same thing. A shade yellows faster on a cheap lamp too, so if you can, pick one with a shade you can replace or clean separately rather than one fused to the fitting.
If you own none and want to start with one, go for a simple black ceramic or metal base with a plain linen or paper shade, nothing with a pattern or a metallic lining to start, that comes later once you know how the light reads in your room. Put it somewhere it earns its contrast, a pale console table, a bookshelf against a light wall, a nightstand next to white bedding. That's where a black lamp actually does something rather than just sitting there being dark furniture.
The detail that makes a good one worth living with is how the light falls through the shade rather than off the base, a warm, slightly amber glow against that black body, so the lamp itself almost disappears into the room at night and all you notice is the light.