Visio attaches the VisDM prefix whenever you link a row from the External Data window to a shape and the shape doesn't contain a field whose name matches a column name in the data row.
You can prevent Visio from attaching the VisDM prefix by creating Shape Data fields in your custom shape in advance. To say that another way, when you create your custom shape, add a Shape Data field with a name that exactly matches the name of each column in your data.
I don't recall at the moment whether the match between the column name and the Shape Data field name is case sensitive, but I think it is. A quick experiment will tell you for sure.