Well, let's say you are saving this 'name' entered by user on a variable named @name.
So, on the controller that do the action of search, you did something like:
if @name
...#action if the name was found
else
session[:name] = @name
...#here is the action you did to redirect
On the declaration of the method called (you said it was 'new') :
def new
@name = session[:name] if session[:name] #I don't know exactly if the condition is this one,
#but you have to confirm that the session was instatiated
session.delete(:name) #to don't let garbage
...#continuous the action of show the new page
#and on the page you have access to a variable @name, that have the name searched before.