No, you don't. Practically any last or this Gen Ryzen 5, 7 or 9, or any last or this Gen Intel Core i5, i7 or i9 is perfectly fine for any existing titles. In fact, depending on your expectations many users are doing quite well with even lower tiered CPUs but for the RTX 4090 I'd stick with either one of the this Gen Ryzen products or one of the this Gen Intel products and I'd go with whatever the best is you can reasonably afford without having to sacrifice too much on the rest of the build if this is a full build.
A 5000 series or 7000 series Ryzen 5 or 7 is plenty good. A 12th or 13th Gen Intel i5 or i7 is plenty good.
Of course, you must also factor in how much multi-tasking you plan to do. If you ONLY run the games themselves without much else running simultaneously then pretty much any modern CPU with between 6-12 cores is perfectly fine. If you plan to do a lot of things at once, like gaming along with streaming, recording, many browsers, lots of mods, many overlays, or whatever, that is when you might want to fudge upwards a little bit in terms of going for a few more cores simply to offset the additional processes you think you will need to run simultaneously.