The first thing I check is where the chain meets the nameplate, right at those two little rings. That join is where every name necklace I've ever owned has eventually let me down, and if it looks like it was soldered by someone in a rush, it will snap within a year, usually while you're pulling a jumper over your head. A decent one has a slightly thicker join there, sometimes a tiny loop of extra metal, and you can feel the difference with a fingernail even if you can't always see it.
Once you're past that, look at what the piece is actually made of, because the listing often just says "gold plated" and leaves you to guess the rest. Gold vermeil, which is a decent layer of real gold over sterling silver, will outlast you if you keep it dry and out of the shower. Plain gold plating over brass is lovely for the first few months and then goes a strange flat bronze at the edges of the letters, usually right where your thumb rubs it without you noticing. Solid silver tarnishes if it sits in a drawer for too long but a jewellery cloth sorts that in under a minute, so I don't hold it against it. Perfume, chlorine and sweat are the real enemies, so I've learned to put mine on last, after everything else, and take it off before a shower rather than after, which feels backwards the first few times you do it. The letters themselves are worth a proper look too, under shop lighting if you can, because cheap ones have rough edges on the script that catch on wool.
Worn daily, a good one settles into something that looks almost like skin, you stop noticing it's there, which is exactly what you want from a piece that's meant to be personal rather than a statement. It goes with almost everything precisely because it doesn't try to do much, a plain tee, a shirt with the top button open, even a jumper if the chain's long enough to sit outside the neckline rather than tangled underneath it. I wear mine with a plain crewneck most days and it just reads as finished, rather than dressed up.
The mistake is buying the name in a font so delicate it looks like thread, because those are the ones that bend the first time a bag strap catches it, and once a nameplate bends once, it never quite sits straight again.