Artist names shows on iTunes but not on phone (very different problem)

It's not clear from your post exactly where the issue lies, so let's start from the basics. The first thing is, is Artist listed in the Library menu of the music app on your phone?

You may need to scroll your screen down in order to see the full list. In my screenshot above, note that the list is between the headings Library and Recently Added. My list does not currently list Artists. To add it to the list, tap on the Edit button in the top right corner, to reveal the following screen:

Tap the Artist button to put the tick on the circle, then tap Done. It will now be on the menu.

Next, you mention "compilations". Compilations have their own set of issues within iTunes, but that's another matter. But one thing to note about compilations is that (for some strange reason) artists who appear only on compilation albums are not listed in the Artist menu. Even with artists who have albums of their own in your Library, if that artist also appears on a compilation album, that album and song will not be listed in the artist's list. (On some previous iPods, it was still then possible to display those artists, but I haven't found a way on my iPod Touch, which in many respects is the same as an iPhone.)

Below are a couple of screenshots of albums, as shown in iTunes, with the tags (fields) required:

This screenshot shows all the tracks selected on a compilation album and then I've clicked on the Edit/Get Info option:

1. the artist field show the text mixed and greyed out, because each song has a different artist.
2. the album artist has Various Artists in the box, which is correct. On Compilation albums, it's important that this field is completed
3. compilation is ticked, because this is a compilation album. Again, on Compilation albums, it's important that this field is completed. However, for Greatest Hits albums, by one artist, this box should not be ticked

Below, is the Edit/Get Info panel for just one of the songs on that album mentioned above. Note the differences:

1. when looking at an individual song on the same album, the artist field has the song's artist name in it
2. album artist still shows Various Artists
3. the compilation field is still ticked

Looking next at an album by one artist:

1. The artist name is shown in this field, because the same artist performs every track on the album
2. Although the artist name is shown in the album artist field, it's not strictly necessary in this case. This field could be blank and it should not matter.
3. the compilation flag is off, because this is not a compilation album

So has any of this helped you solve your issue?

Try Grouping tracks into albums for general advice. I would recommend completing both Artist and Album Artist. You may need to remove tracks from the device and add them back again for some changes to be processed properly. The compilation flag should only be used where it is also appropriate to use Various Artists as the Album Artist. It may help to go into specifics with a particular album that doesn't show the way you expect to see if there is a way to do what you want, or you are up against a limitation of the platform.

tt2

Have you tried removing the tracks from the device and adding them back in separate sync operations. Since .wavs don't carry a tag the metadata you enter is stored in the library and the file isn't updated when you make a change, so the file modification date won't change, and iTunes won't necessarily recognize that it needs to transfer new information. You might consider a lossless conversion into Apple Lossless format which will allow for embedded metadata including artwork.

tt2

Another possibility comes to mind. See Multiple tags (MP3 files only).

tt2