In the bowl of an electric mixer fitted with a paddle attachment, mix together the butter and 1 cup of sugar on low speed until they are just combined. Add the vanilla. In a medium bowl, sift together the flour and salt, then add them to the butter-and-sugar mixture. Mix on low speed until the dough starts to come together. Dump onto a surface dusted with flour and shape into a flat disk. Wrap in plastic and chill for 30 minutes.
Roll the dough 1/2-inch thick and cut with a 4 1/2-inch hammer-shaped cutter. Place the hammer cookies on an ungreased baking sheet and sprinkle with sugar. Bake for 20 to 25 minutes, until the edges begin to brown. Allow to cool to room temperature.
For the icing, combine the confectioners' sugar and corn syrup in a bowl with a wire whisk until it is a thick paste. Gradually add enough lemon juice until the mixture is a good consistency for piping.
With an extra fine pastry tip, pipe individual names on the hammer cookies. Let the icing set before serving.