Jelly, 74  65 bytes

“ÆÇÐÑ÷øœ‘Ṭœṗ⁸ṙ©-¤4421œ?U0¦;"⁷,⁶ẋ⁵¤¤ṁ9¤ȮœS.®ß
“9ɲcḟ#%⁴1t(ŀȷUCOw⁾»Ç

Windows version running in a 6 line high cp-65001 console.
There is a half a second (plus evaluation) pause between iterations:

How?

“9ɲcḟ#%⁴1t(ŀȷUCOw⁾»Ç - Main link: no arguments
“9ɲcḟ#%⁴1t(ŀȷUCOw⁾»  - compression of [d( Happy)+d( birthday)+d( Raff)+s(aele)+d( Ce)+d(cc)+s(o)] - d=dictionaryLookup, s=stringEncode.
                     -              = " Happy birthday Raffaele Cecco"
                   Ç - call last link (1) as a monad

“ÆÇÐÑ÷øœ‘Ṭœṗ⁸ṙ©-¤4421œ?U0¦;"⁷,⁶ẋ⁵¤¤ṁ9¤ȮœS.®ß - Link 1, rotate, print, recurse: string s
                ¤                            - nilad followed by link(s) as a nilad:
            ⁸                                -   link's left argument (initially s)
               -                             -   literal -1
             ṙ                               -   rotate left -1 (e.g. "blah" -> "hbla")
              ©                              -   copy to register and yield
“ÆÇÐÑ÷øœ‘                                    - literal: [13,14,15,16,28,29,30]
         Ṭ                                   - untruth: [0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1]
          œṗ                                 - partition right at truthy indexes of left
                                             -   chops up the rotated string into 8
                                             -   e.g. [" Happy birth",'d','a','y'," Raffaele Ce",'c','c','o'])
             4421œ?                          - get the 4421st permutation of those items
                                             -   e.g. [" Happy birth",'o','d','c','a','c','y'," Raffaele Ce"]
                         ¦                   - apply to indexes:
                        0                    -   0 (right most)
                       U                     -   upend  (e.g. " Raffaele Ce" -> "eC eleaffaR ")
                                     ¤       - nilad followed by link(s) as a nilad:
                                  ¤          -   nilad followed by link(s) as a nilad:
                                 ¤           -     nilad followed by link(s) as a nilad:
                              ⁶              -       literal space
                                ⁵            -       literal 10
                               ẋ             -       repeat: "          "
                            ⁷                -     literal new line
                             ,               -     pair: ['\n',"          "]
                                     9       -   literal 9
                                    ṁ        -   mould like: ['\n',"          ",'\n',"          ",'\n',"          ",'\n',"          ",'\n']
                           "                 - zip with:
                          ;                  -   concatenation
                                             -     e.g. [" Happy birth\n","o          ","d\n","c          ","a\n","c          ","y\n","eC eleaffaR           ","\n"])
                                      Ȯ      - print and yield
                                         .   - literal 0.5
                                       œS    - after sleeping right seconds yield left
                                          ®  - recall value from register (s rotated by 1)
                                           ß - call this link (1) with the same arity (as a monad)