Ch-ch-ch-changes! I myself just colored my hair a shocking shade of red after being bleach blonde for the past year. Sometimes you gotta keep 'em guessing, I suppose.
This question is one I've been posed several times, so let's dive right in.
Firstly you do not HAVE to change your makeup because you colored your hair. Your skin is still the same...you still have the same features...eye color...you get the picture. Your hair doesn't make your entire look, but it can be a great idea to switch up your makeup for the following reasons:
1. Your hair color can affect how your skin looks. You might've noticed that going blonde can give drain you of color and make you look a bit 'washed out'. The opposite holds true for choosing richer, warmer colors, which might make your skin look warmer than it did before. If you notice one of these changes, you might want to tweak your makeup just a bit. If you feel paler with your new color, try using a bronzer (like this one I love from Too Faced) to bring a little life back into your skin. I've got a great bronzer tutorial if you're feeling clueless. If your skin is a little warmer than it used to be, that's great because it'll make you look more healthy and alive. You don't really need to make any makeup changes, but you can play around with using warmer bronzes on the eyes or warmer shades in general to go with your complexion.
2. You want to compliment the color of your hair. If you're really loving your new hair color, you can compliment it by using colors that are the opposite of you hair on the color wheel. For blondes (which have yellow tones), choose light purples or plums for your eyes. For red heads, golds and greens will add some pop. For brunettes, you can go either way depending on if you have more red or gold tones in the brown. Keep in mind your hair color itself won't really change appearance based on your makeup. The idea is just to create a copacetic color palette.
3. You just plain want to change your vibe! Obviously if you changed your hair, you were probably feeing a certain mood fo your look. Use this as an opportunity to reflect that mood in your makeup as well and try something new! Maybe go for softer, more feminine looks if you went blonde...or ramp up a caramel hair color by doing the whole J Lo-monochromatic-bronze-makeup-thing. If you went uber dark, maybe it's time to try a bold lip. Venturing outside of your comfort zone might be a little easier now that you've already made another big change.