Not all children were named after relatives. Our ancestors typically had many children, and since infant mortality was high, they often ran out of deceased relatives to memorialize. Therefore, sometimes other sources were used. A child born on Purim might be called "Esther" or "Mordechai" (the heroes of the Purim story); one born during Passover could be called "Pesach"; or "Shabbatai", if born on the Sabbath; or "Nison", if born during the Hebrew month of Nisan; and "Chanukah" apparently is a popular name among some Sephardim.
One should not, however, try to draw too many conclusions from such a name. The birth that resulted in a 'holiday' name may have occurred many generations earlier: a man named "Pesach" may have been named in memory of a grandfather named "Pesach" who was born during Passover, etc.