A fact from University of California, Santa Barbara Library appeared on Wikipedia's Main Page in the Did you know column on 1 August 2011 (check views). The text of the entry was as follows:
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"University of California, Santa Barbara Library" is an awkward title (makes it sound as if it's the branch of University of California that is located at 'Santa Barbara Library'). Something like "Library of the University of California, Santa Barbara" is less ambiguous, although that is just something I made up. Their website calls itself "UC Santa Barbara Library", which is probably the closest thing there is to an "official name" and is less ambiguous than the current one; I think using that abbreviated form would be preferable to the fully spelled-out name (which is not actually used anywhere, as far as I can tell). rʨanaɢ (talk) 00:46, 27 July 2011 (UTC)[reply]
True, but the name of the university does include the comma (University of California, Santa Barbara). In a case like this (with no official name), I would tend to look at usage and formality. Here's some numbers run through Google:
"University of California, Santa Barbara Library": 399,000 hits
"University of California, Santa Barbara Libraries": 5,400 hits
"Library of the University of California, Santa Barbara": 217,000 hits
"Libraries of the University of California, Santa Barbara": 3 hits (but, notable, does include two references in academic journal articles)