The name "Songbird" was previously used by Mozilla, a large, well-known and fairly wealthy organization which is still around and has a world-famous product. It therefore probably has trademarks on the name. Debian, famously, had to maintain its own forks of Firefox and Thunderbird for many years because the Mozilla terms of use on the names and icons were incompatible with the Debian IP guidelines.
Mozilla itself, as I pointed out, had to change the name of what is now its flagship product _twice_ because other software companies used and owned the names: Phoenix is a brand of PC BIOS, Firebird is a database.
Mozilla _might_ have released the name as the product is dead, but it would be foolhardy to rely on this.
If the new project succeeds and prospers, then Mozilla will notice, and as Mozilla had the name first, the new project will have to change it. This is a pain and can be detrimental to awareness, community etc.
Songbird was a high-profile product at the time. As a user of Netscape and Mozilla products since 1996, I ran it myself for a while. (I decided it was way too bulky for a media player.) Thus I am surprised it has been so forgotten so quickly, as apparently have Mozilla's repeated forced name-changes.