Is there a way I can modify the Field Name or to make him keep the Alias when a table is exported?
Or is there a way to keep the Alias instead of the Field Name, when exporting for example to .dbf ?
I want to be able to do this in ArcMap.
If you use the ArcToolbox Tool "Table to Table" you can add, rename, or delete output fields using the Field Map Parameter. With arcpy you can use the tool and build your own field map. That field map can use the aliasName property of the field object (have a look at the FieldMappings example 2.
With ArcGIS 10.1 you are able to rename the field name in ArcCatalog (table properties), if your data source is a FileGeodatabase.
The most reliable way to do this in ArcMap is to use the Table to Excel (Conversion) tool, making sure the Use field alias as column header checkbox is checked: