Have you considered VLOOKUP() or an INDEX()/MATCH() combination?
Here's how to use a VLOOKUP():

1. Create a backup of your data so you can recover from a disaster.
2. Insert a new tab called "Reference" in your spreadsheet, and create
a table like this one, in the range A1:B6 :
Hospital Nurse
Hospital A Ann
Hospital B Brianna
Hospital C Claire
Hospital D Denise
Hospital E Elizabeth
3. In your main sheet, column J, where you need a nurse's name, enter
this formula:
=VLOOKUP(A2,Reference!$A$2:$B$6,2,0)

If you go this route, you'll need to expand the range in your formula
to accommodate the rows in your Reference table. This should do it for
you. Have a good weekend!