I have a Nokia Lumia 620, when I add music to my phone from my computer, it copies the songs over fine but the phone does not recognise the artist even though the information is there.
I had the same problem on my Lumia 920. Turned out it was caused by the tags being written into the MP3 files in an "old" standard (of the tag format definition). I downloaded this software and updated the tag information (by hand) in the MP3s and fixed the problem (there is a dropdown that specifies the tag format version for each file).
I'm sure there are other packages available - a utility that automatically changes the tag format on all files in a folder would be really useful (but I stopped looking when I found my solution - maybe you'll try harder than I did).
You can get the artist/song name by changing the meta data in your file explorer. For Windows you just click on the file so it is highlighted then edit the boxes at the bottom.