Using the Phanteks Enthoo Evolv ATX, the major parts are compatible and good to go:
MB - ATX size - check (case supports ATX)
CPU Cooler - 166.5mm height - check (case supports up to 194mm height)
GPU - 279mm length - check (case supports up to 300mm length with the HDD brackets installed)
One particular height clearance you may wish to check is the CPU Cooler against the RAM. The V8 GTS is a large cooler taking up to 154mm in total length. There is a great chance it will go over some RAM slot/s. The Vengenace LED sticks are about 49mm in height. If I'm not mistaken, the V8 GTS has about ~50mm (not sure) clearance beneath the heatsink/fins. There's a great chance the RAM will fit under that space, but depending on the actual distance of the DIMM slots of your Maximus IX Hero from the CPU, it might look like this (note that this is not the same motherboard as you have selected):
Another particular part that I wish to suggest is replacing that initially selected PSU (EVGA SuperNOVA NEX 650W 80+ Gold) with a higher quality one. The NEXG series is somewhere of a mediocre (middle-tiered category) PSU. Since you'll be building a high end rig, it is proportionate to also select a higher-tiered PSU. Note that with your i7-6700K + single GTX 1080 build, a good quality PSU supplying 520W (or 550W for a bit more headroom) is more than sufficient. You can also get a good quality 620W (or 650W) PSU if the price is right. I suggest looking into the Seasonic G series, Seasonic X series, XFX XTR Series, XFX Pro Series, EVGA SuperNova G2 or GS Series, or Corsair AX or AXi or RMx or RMi (not the RM) series, whichever fits your budget.
For the case fans, the Phanteks Enthoo Evlov already comes with 3x pre-installed 140mm high quality fans (although they don't have bling-bling LEDs). Two are pre-installed at the front while one is pre-installed at the rear, leaving you with just the top slots capable of mounting either 2x more 140mm fans or 3x more 120mm fans. It's up to you if you wish to retain the pre-installed Phanteks fans. If you do so, you will only need to buy either 2 sets of 140mm LED fans or 3 sets of 120mm LED fans. You can replace whichever pre-installed fans as you please. Note that the front fans (with the 2x pre-installed 140mm fans) can also fit 3x 120mm fans in case you wish to replace everything with LED Riings.
For the ODD (Asus DVD/CD Writer), you won't be able to install that as the Evolv does not have any external 5.25" bays. So, if need a DVD/CD writer, you should purchase an external one.
Other than that, you're good to go.