Through searching I found that in UML, aggregation(assuming that it's used properly) can be used to represent attributes in a class.
(Assume column can stand alone)
Then, using such example, if I want to replace the attribute: Column[] with map to represent the column's name, would it be correct to use an association class just like below? (In case, I'm not willing to put the column name in Column class as an attribute)
Association classes are used with simple associations. They have m-1-1-n multiplicity. The shared aggregation (as you used) has no defined semantics (and I recommend to simply not use it unless you have a domain specific and documented use for it). It's simply better to put the intended multiplicity on either side of an association.
An association class connects two classes, adding attributes and/or operations. Your example is "unconventional" since Table/Column have a simple relation which would not need an association class. A general example is the Student/Lecture relation where you can put an association class in between to record exam results, times etc.