God shows himself to Moses. He describes himself as a loving compassionate God yet he still punishes the guilty. Some say God changed between the old revelation and the new. But I do not believe so. I believe God still punishes the guilty, even me. But he forgives iniquity, transgressions, and sin (34:7) first and foremost. I think God does it to help us, not hurt us. Without some punishment we would go crazy. And God sends his Holy Spirit to be a reminder of what is right and good.
God is gracious and compassionate. He repeats this several times in 33 and 34. And "God's characteristics of love and mercy are held in perfect tension with his judgment of sin." - Richard Harvey.
God uses his personal name here, written in Hebrew YHWH, all consonants because in old Hebrew only the consonants are written. You must know which vowels go in between. Because the Israelites and Jews thought God's name too holy to actually say we really do not know how it was originally pronounced. It is God's personal name. Only his friends would actually say it. Otherwise they would replace the word with the word for "Lord". Like we might use the word "sir" or "mister".
Moses says, "If now I have found favor in Thy sight, O Lord, I pray, let the Lord go along in our midst, even though the people are so obstinate, and do thou pardon our iniquity and our sin and take us as thine own possession." (44:9) God agrees to make a covenant with them under these condition but he requires them to destroy pagan altars and worship no god but Him. "For you shall not worship any other god, for the Lord, whose name is Jealous, is a jealous God." God is still a jealous God. He demands that we worship no other god. To me that means nothing else, not sports, not food, not women (or men), not money, etc. And I believe we receive correction when we do.