Well, you're talking about two different things here. You may very well have tagged them properly, however, what you see when you open a folder on your hard drive are the file names--two different things. One of the conveniences of a tagging program such as Tag & Rename is that it allows you to sync file name to tag or vice versa (if one happens to be correct and the other is not or blank). Edesilva is correct, tags are actually metadata and a part of the data file itself--a totally separate entity from the file name. Without an adequate tagging program (lots of software has POS tagging built into it--although not all are horrible) you'll need to do what you previously did in mediamonkey or whatever it is you're using, and then manually change the filename. A whole lot of work...
Even if the cd is tagged perfectly, EAC only gives you so many fields in the tags to fill out. Dedicated software gives you all sorts of options. Some are very useful, especially for classical music (e.g. composer, comments, orginal artist etc.) others... mood (in addition to genre), beats per minute etc. A few programs are starting to emerge that allow you to search and categorize based on some of these odd fields (for example, you feel like head banging and want music only >100bpm)
There are plenty of other advantages such as running macro's on your music as a whole to perform actions such as capitalize the first letter of every word. The programs take some time to learn, but are invaluable once one's collection starts to grow. Personally I use Tag & Rename. It is the easiest, IMHO, to learn--there is more more "powerful" tag editing software, but the steep learning curve and the fact that 1 out of 1000 people will require those functions causes me to recommend Tag & Rename.
