Why do some of the names entered show up as firstnamelastname and others as last name, first name on my reports?
Can you provide on which reports you getting them different? Normally the contacts sort name is used to display on all reports. The way it need to be stored is defined in Administer -> Customize Data and Screens -> Display Preference.
They will appear in your report in the way the data is stored in the database. You may need to clarify what you have to get a better answer. But I would expect that if in your report you have
showing, then that suggests your data itself needs sorting, maybe someone did a strange import?