Does the term ‘Name of the Lord’ in Ex 20 and Lev 22 refer to more than its literal meaning?

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We read in Lev 22:32 (NRSVCE):

Thus you shall keep my commandments and observe them: I am the Lord. You shall not profane my holy name, that I may be sanctified among the people of Israel: I am the Lord; I sanctify you

And we read in Ex 20:7:

You shall not misuse the name of the Lord your God, for the Lord will not hold anyone guiltless who misuses his name.

Israel addressed God in different ways: Lord, God, Yahweh, Redeemer, Almighty, etc. But does any of those terms really stand for ‘Name of the Lord’ as referred to in Ex 20 and Lev 22? In other words, does the term ‘Name’ imply much more than its literal meaning, given that the heathens also used the same or similar words? My question, therefore, is: Does the term ‘Name of the Lord’ in Ex 20 and Lev 22 refer to more than its literal meaning? Inputs from any denomination are welcome.