Divorces were handled the same then as they are now, the plaintiff files, and if the respondent does not argue, the judge signs what the plaintiff submitted to the court. Much like court motions. Both sides submit their motions, and the judge signs the motion he agrees with. The divorce decree was made public, if the marriage license was not in it (which it wasn’t) then the judge did not read it.
“That Libellant and Libellee were lawfully married in Wailuku, Maui, State of Hawaii, on February 2, 1961 by a person duly authorized to perform marriage ceremonies and ever since that date have been and are now husband and wife.”
“That Libellant and Libellee last lived together as husband and wife in Honolulu, Hawaii but are now living apart.”
“That one child has been born to said Libellant and Libellee as issue of said marriage, to wit: BARACK HUSSEIN OBAMA, II, a son, born August 4, 1961.”
http://www.scribd.com/doc/12234409/Divorce-Decree-1964-13-Pages-Merged
Additionally The state of Hawaii Office of Health Status Monitoring’s Marriage Index for 1960-1965 lists the Dunham-Obama marriage.