gridview can be binded using a datasource.
gridview1.DataSource = methodToRetrievefromDB(DropDownTableName.SelectedValue);
you'll have to apply checks for Table to retrieve records from and execute the procedure for the selected table.
On change of value of drop down you must retrieve records each time. You can store both tables in a temporary space and use that if you want to avoid hitting DB again and again but it depends on the number of records and tables.