It was recently found out by coincidence, but if you go to Jasrac's website
http://www2.jasrac.or.jp/eJwid/main.jsp?trxID=F00100
and type in ステラグロウ (the Japanese title) into the product name box, it will bring out the registered BGM for the game that Jasrac owns(?)
Since there is no soundtrack or in-game music room, this was actually the first time people found out the official names for the titles of the BGM.
That said, there is nothing that indicates what the BGM is for, as the only information is the title. Though some can be guessed. Here they are:\
PS: Sometimes the font goes weird because I copied the text and Blogger did stuff with that font
PPS: I might organize this in a better documented manner tomorrow or so
UPDATE: Added documented version of BGM titles. Please click to enlarge