Is it permissible to replace an old tattoo that contains immoral drawings with a new tattoo bearing the person's name, if the old tattoo cannot be removed due to the harm it would cause?

It is not permissible to replace an existing tattoo with another. If it is possible to remove the tattoo by permissible means and without harm, then one should do so. Otherwise, one should leave it and repent to Allah. Furthermore, one should not display the tattoo to people if it contains immoral imagery.