As for the only Beatmania I own, the PAL PSX version, it's quite an inconsistent mix of "beat mania", "Beatmania" and "beatmania" on the back cover and "BEATMANIA" on the spine. "Beatmania" is used all throughout the manual, except for the Dutch part, where it's always "beatmania".
The ingame logo most likely says "beat mania". The space between both words is quite small, however, so I'm not 100% sure. MAME uses "beatmania", btw, so there might not be a space after all.
beat mania (separate)
1, 3rdMIX, 5thMIX, GOTTAMIX, GOTTAMIX2, The Sound of Tokyo!
4thMIX, 6thMIX, Dreams Come True, ClubMIX, Best Hits