No, there's no way to affect the default behavior of the FormulaBuilder like that. You coul, of course, edit the formula yourself and just delete the parts you don't want.
Formulas in the FormulaBuilder use relative references whenever possible. So how the column reference is specified depends on what object you are setting the formula of. If you apply a formula to a grid column and you reference another column in the same band, then the formula builder should just use the name of the column. But if you refer to a column in the grid from some other control like a textbox or from a named reference, then the name must be fully-qualified in order to be recognized by the CalcManager.