To use a different kernel, for example do:

  (kernel linux-mine)

  (initrd (lambda (file-systems . rest)
              (apply base-initrd file-systems
                                 #:linux linux-mine
                                 rest)))
                                                    
in your operating-system form.  A starting point for an alternate kernel
definition:

(define-public linux-mine
  (package
    (inherit linux-libre)
    (name "linux-mine")))