The title Katamari Damacy is a transliteration of "Katamari Tamashii" (塊魂). "Katamari" is japanese for "lump/clump" or a "mass", and "Tamashii" is "soul/spirit", which roughly translates the game's title as "clump of souls", in a context of "team spirit." The two kanji-letters also look similar, using similar right-side letters (akin to 鬼).
When asked about the title, Keita Takahashi (director and producer for the first game and following sequels) said in an interview with Dengeki Online "It just popped into my head suddenly, and this is what it has been from the beginning."

In the game's final level "Make the Moon", a small island can be found and rolled into the Moon called "Demo Island" with the description: "You can play for free, but they won't fix anything if there's a "Technical Issue"." This island is a replica of the map used in a Katamari Damacy demo disc that was shown off and given to attendees at Tokyo Game Show 2003.