Q. Is the name of the reference counted in the word count?

If you are using an in-text based referencing format, such as Hull Harvard or APA, your in-text citations (the bits in brackets) are included in your word count. 

The reference list or bibliography at the end of your assignment is not included in your word count.

There may, of course, be exceptions so you need to check your module handbook or check with your tutor to make sure.