Changing the field name should be easy in ArcGIS Pro. The link and video below show how to do it quickly. I propose an alternative method for exporting your layer to answer the situation presented in the forum thread below. See all the steps below:
1. Right-click on your layer -> Data -> Export Features and expand the Fields section. You will see all the fields included in your layer. You can spot two signatures on the right by highlighting one of them. The left one is for editing (the pen), and the right one is for deletion (the “x” symbol) (Pic. 1).

Once the pencil signature is clicked, the Field Properties dialog window opens, where you can find the crucial properties of your attribute field, including Field Name, Alias, Type, Length, and the Allow NULL option. All of them are editable at this stage. See below how the column name can be changed quickly from this dialog (Pic. 2).

You must click the Field Name box and replace the existing name (A). When done, this name will appear on the list (B). The source field name highlighted in faint blue will always remain because it reflects the given field’s circumstances. You can quickly change the field Alias and choose the Type if required. Other options are also quickly doable.
When you change all the columns you want, the layer can be exported. To do so, click OK in your Export Features panel.
3. After exporting the layer, right-click the new one ->Data Design -> Fields and look at the new field properties defined upon the export stage (Pic. 3).

The fields bound in red have both names and aliases changed. As you look a bit above, there is the Handle field, where only the Field Name was edited. The process itself is simple and can work as an alternative.
Mariusz Krukar
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