When praying 3 rakat witr: I was thought from childhood to say i intend to pray "salat shafa-e" for the 1st 2 even numbered rakats and then "witr" for the odd or 3rd rakat. but in our online discussion i don't see any mention of shafa-e when discussing witr prayers. what's the reason? Quran [89:3] mentioned وَالشَّفْعِ وَالْوَتْرِ.
Concerning salat shafae, it is a name of all salat you pray after the last prayer of a day ( ichaa) beginning by 2 rakaat to 8 or 10 for maximun and shafae in arabic means pair (2 rakaat) so in this salat every 2 rakaat must be preced by tachahoud and taslim.
After the salat of shafae you must pray the witr salat which mean in arabic odd it can be 1 rakaat or 3 rakaat without tachahoud in middle or 5 or even 7 and the prophet PBUH have prayed it in 4 kinds I've told you.
So the 3 rakaat you are praying if you do tachahoud and tasslime in the middle it is shafae(2)+witr(1) but if you don't do that it is only witr(3).