Should (boundp object) be tested and what would it mean

Have made this function This function to tell me the symbol name 
of the type of object being passed.

Should one test for (boundp object) and what would that mean exactly? 

(defun lana-obnam (object)
  "Return variable/symbol NAME holding OBJECT."
  (cond
    ((symbolp object)  (symbol-name object))

    ;;((boundp object)  (something)) 

    ((hash-table-p object)  "hash-table")
    ((plistp object)        "plist")

    (t  (format "%s" object))))