‘ “And you will know that I am Yahweh when I have wrought with you for my name's sake, not according to your evil ways, nor according to your corrupt doings, Oh you house of Israel,” says the Lord Yahweh.'
Note the repetition of ‘you will know that I am Yahweh'. Compare Ezekiel 20:5; Ezekiel 20:7; Ezekiel 20:12; Ezekiel 20:19; Ezekiel 20:26; Ezekiel 20:38; Ezekiel 20:42. God had been revealed as He is in His mighty deeds in past days, and He will be revealed so again. All that He had done and would do was so that men may know Him as He is. What mattered was the full revelation of God, for thereby would man enjoy his greatest blessing. So God would do all this for His own name's sake, for by their behaviour and their doings the people were totally unworthy of it.
It should be noted that there is no hint here of the rebuilding of the Temple. That was not what was important to God, although it may be seen as intended in a secondary way to be included in the comments about the offerings, the firstfruits of their oblations and the holy things.