Merge rows based on Levenshtein distance

I am new to PostgreSQL and I have the following table:

Name, City
"Alex", "Washington"
"Aleex1", "Washington"
"Bob", "NYC"
"Booob", "NYC"

I want to "merge" similar rows based on levenshtein distance between names
so that I have the following table:

id, Name, City
1,"Alex", "Washington"
1,"Aleex1", "Washington"
2,"Bob", "NYC"
2,"Booob", "NYC"

How could I do that on PostgreSQL? Is there an SQL command for this?
Thnsls




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