There's nowhere in photoshop that will show what your current monitor profile is set to. Since it is a color aware application, it will use whatever you have set in windows color settings as the defualt for your monitor, which the Asus utility *should* set automatically (it does on my mac, but the first few versions didn't generate an icc profile at all, they're definitely still working on that software). The color settings in photoshop are for your working space, for which you do not want to use your monitor profile, you should be using something well behaved like AdobeRGB, sRGB, etc-- something that is meant to be a working space, not a device profile. IMO I would also advise that you turn on all the check boxes for warnings for missing embedded profiles and profile mismatches and deal with them on a case by case basis. I've worked with colleagues who refused to turn on those pop ups, and it was fine 95% of the time, until we had someone who wasn't knowledgeable send files through without embedded profiles, and then the files were being worked on for hours without any indication that there was a massive color change when opening the file initially.
Having it show up in the "convert to profile" list is not relevant here, except to check that you have actually generated a working icc profile from your profiling software.
But long story short, it's all about getting the profile properly activated in windows color management (or colorsync on mac). The settings are not within the adobe suite.
