Usually, you'd have to convert a Mac font for use under X11 (with some exceptions). Not the least problem involved concerns the types of font each can work with. The main problem here is that OpenOffice runs under X11 which has quite different font setup, installation and management than Mac OS X. I'm not sure a font manager would help with this, but I've never used Linotype so perhaps it has special integration functions. It might be picking up a preference setting from an earlier installation, but the main point is that I seem to have access to fonts from /Library/Fonts as well as /System/Library/Fonts though not, I think from my user collection of fonts. If you have the latest stable version, when you first opened it you should have been asked two font-related questions: do you want to use the system fonts? and do you want to use fonts you've installed? I answered yes to both and the application opened an empty document with Times New Roman as default.

Which version of OpenOffice are you using? Font management on OS X has changed, I believe.

It sounds as if you're seeing the System fonts from /System/Library/Fonts and not from /Library/Fonts.

Fonts for openoffice