Two things usually contribute to songs not appearing under Artist on an iPod, both are due to information either in or missing from the Get Info>Info tab against the song in iTunes. 1) the song is marked as part of a compilation or 2) it is missing an album name. If the tracks are ticked in the Get Info>Info tab as part of a compilation, they will not appear under Artist on the iPod. Highlight a song you know is not appearing, from the iTunes File menu, choose Get Info and click the Info tab, if "Part of a Compilation" is marked untick it and afterwards update your iPod, you'll find it now appears as normal. Compilations are stored in a separate folder in iTunes so the songs don't appear inside the normal Artist>Album folder, this means therefore they don't transfer over in the same way. Also it could be that the tracks are missing an Album name in the Info tab, this information needs to be filled in, in the absence of one you can just add None or Miscellaneous. See this link:
I don't see some of my songs when browsing by artist on my iPod