The same name for 200 records? While you can do that, it sounds like something a change in how you design your database would completely avoid and this could be a much better approach for you.
To answer the question specifically, you can use replace field contents to enter the same value in all the records in your found set all in one go. This can't be undone so read up on this feature in FileMaker help and save a back up copy of your database before you try it out.
Where can I back it up? I dont even see a place for save or save as, I only see save as exel, or pdf. Where do I go to replace field contents?
Use Save a copy as in the File menu.
You can also close the file and use your operating system to make a copy just like you would any other file on your computer.
And since you want to enter the artist's name over an over, you might also consider setting up a table where you have one record for each artist where you'd record the name as well as any other inform specific to that artist and then link that table to your existing table by an ArtistID so that you don't have to enter quite as much data over an over again in your existing table.