This can be done with a script. Enter the following in Script Editor, found under Tools. Change the 'Name' to whatever is the name of the form field that should be used.
function formSheet(e) {
var sheetName = e.namedValues['Name'][0];
var sheet = SpreadsheetApp.getActiveSpreadsheet().insertSheet(sheetName);
sheet.getRange(1, 1, 1, e.values.length).setValues([e.values]);
}
Then set a trigger using "Resources -> current project's triggers" in the menu. It should be "from spreadsheet", "on form submit".
This function also copies the submitted value to the first row of the new sheet.
Note: there cannot be two sheets with the same name, so if some name is submitted more than once, sheet creation will fail.
References: Event object, Sheet class methods.