If XSSFWorkbook.setSheetName() is called when you have named ranges set in the workbook, any absolute ($A$1) references in the named ranges are replaced with relative (A1) references. I suspect the problem is actually caused by XSSFFormulaUtils.updateName(), which is called to update references to the sheet.
Any chance of a piece of code which reproduces the problem? Preferably as standalone unit-test...
No response for a month so we cannot really work on this, please reopen with more information if you can provide some sample code.