Thread color is harder than screen color. There's no CMYK-to-thread converter that gives you a perfect match. Brand colors need to be specified per thread manufacturer, and even then two threads with the same code from different suppliers won't match exactly.
Start with a printed color card from your thread manufacturer of choice — Madeira, Isacord, Robison-Anton and Sulky all publish reference books. Match your Pantone chip against the actual thread, not the printed swatch, under daylight. Pick the closest thread and record its code.
For consistent runs, stick with one manufacturer and one product line per project. Madeira Classic 40, Isacord 40 and Robison-Anton Rayon are all excellent but not interchangeable.
If you're a digitizer delivering files to clients, always include a color chart naming the specific thread codes. This is one of the small professionalism touches that saves customers from playing thread-matching guessing games.