Most of my music was brought in from sources other than i tunes, so i have a ton of inconsistsncy in naming and labeling. But even when the artist name looks the same on the itunes list, it may look different to the computer. The number of spaces after the name, hidden characters etc. anyway...
In i tunes, get all the songs on the same page (dont really need to have them on the same page, but it makes it much easier)
Then highlight the list. A box should pop up, the top entry says 'get info'. If the box does not pop up, right click to force it.
Click get entry, and it will ask, are you sure you want to change all these songs. Tell it yes, and a screen with each of the available info fields will appear. Only make an entry in the field you want to change. In this case, artist. Type it how you want it and push enter. It will change that field for all of the songs that you have highlighted to that which you typed. Do not horse with song title or album name, as you will overwrite what was already there.
This is also a good time to get your genre set the way you want if, if you care about that.
Try it on a short list once or twice so that you get the technique down. I have about 7000 songs, and this is clearly not something i can clear up in a day.