How to create a column Alias?

There are two things people mean by this, and it is worth separating them.

To rename the field, double-click it in the Data pane or in the metadata grid on the data source page and type a new name. The underlying column is untouched; only the display name changes.

To rename the values inside a dimension, right-click it and choose Aliases. That opens a table where each member can be given a display name — `CA` shown as `California`, for instance.

Aliases apply only to discrete dimensions, and filters and joins continue to operate on the real values, so nothing downstream breaks.