Although there is now a shampoo called Rejoice, and every shampoo is supposed to be something at which one rejoices, the more sane, or conservatively educated, person associates the phrase "Rejoice greatly" primarily with "Rejoice greatly, O daughter of Zion" (Zechariah 9:9–10) from the Bible, and the coloratura soprano aria of that name, which is a musical setting of those words, in the Messiah by Handel. Please look it up - both the Bible and the video of the aria.
It is not such a good idea to use it with your dog.
I think people (journalists) use "rejoice greatly" to describe moments of political and sporting victory, of religious contemplation and worship, and of personal affection.
Don't be a shampoo commercial. Use "rejoice greatly" sparingly and advisedly.