You can’t change the background colour as there is no background in Adobe Illustrator, one thing you could do is change the colour of your artboard, to do this:

From the File menu, scroll down and select ‘document setup’. In the document setup dialogue, select ‘transparency’ then ‘simulate paper’, click on the top grid colour swatch, and you can choose a new colour with the colour picker there. This will change your artboard colour for this document only. Changing your artboard will not have any printing affects.