Here is an approach that has worked for me: start with a finishers color wheel which gives a directional sense when placed against your target (is it more of a green brown or red brown? etc). Transtint has a color name conversion on their website. I then do very small batches of dye on a piece of same wood, same wood prep. For example “x” drops of dye A and “y” drops of dye B. Line up the ratios and dye choices on the wood and label. Often this is a mix of dyes based on the directional guidance from the color wheel. Compare the dye samples with your other piece. Some will stand out like a sore thumb and others will get close. Refine your mix and when happy make a sample with the full finishing schedule including topcoat on the target wood prepped the same. Scale the dye ratio for larger batch. It’s time consuming but it works for me.
To be sure, there are other ways to go about matching. Also consider how committed you are to a match vs the roughly the same color value.