Hi Herman,
only by changing the code - the problem is that the booking form is dynamic, so we don't know what your fieldnames for firstname / lastnames are (and if you even have some) - second problem is that Joomla names are first- and lastname combined while Matukio has single fields for first and lastname (We tried a split regex with the space but that did not work out for many users).
If you don't need any of these fields (because it's supplied by the Joomla user) you could try using the "old" simple booking form (The email and name are automatically used when you are logged in there).
You could also adjust the code a bit to automatically use the Joomla users data (JFactory::getUser()->name etc.), with the above explained disadvantages.
Best regards
Yves