Is there an easier way to change our names than pay $500 in court fees for a name change petition?

We got married within the past year and wanted to change our last name to a new last name by merging them. For example, if my last name is Compete and hers is Lete, having the new last name Complete. We researched taking a new last name and some sources said this is possible. We made sure to tell the marriage court this is what we wanted and they said we would be fine changing this at the social security office. We went to the social security office and they said that the marriage certificate has to list the new last name and it is not possible without this. We researched this https://secure.ssa.gov/poms.nsf/lnx/1502712016 and the law seems to be conflicting that they allow changes to an entirely new last name but it must be listed on the marriage license form however Illinois does not offer a section on the form but some other states.