My alma mater university is University of California Santa Cruz (UCSC). I and others (locally, some of us affiliated with the university as students, faculty, staff, alumni, community members with other university affiliations…some not) have carefully mapped both the “main campus” and other localities affiliated with UCSC in OSM. The main campus is (certainly correctly) tagged amenity=university. There is also a “Marine Sciences Campus” (bordering the ocean) further south along the coast which also houses / hosts (federal and state) government agencies (in buildings, with government staff) which are involved in marine science / marine research / marine protection — this is where a sense of “university / government (at multiple levels) overlap.” There is also a “pure research” genetics laboratory (and others) nearby (at Antonelli Pond) which are also “off-campus” (of the main campus), though located in a “campus corridor” (of the northern and then along the western edge of Santa Cruz California).
Additionally, there are also nearby (off-campus of the main campus) administrative (non-student / classroom, non-research / classroom) UCSC “offices” nearby which administer things like campus payroll for faculty and staff. Most people, even if they are affiliated with the university, never have anything to do with this building / site, unless you happen to work there as, say, a university payroll processing worker.
Finally (or is it?), there is a “commuter campus” in Silicon Valley (about 60 km north) which caters to students who are “geographically based” in the “South Bay” (Silicon Valley area) as this is a more convenient location for certain technology-based classes to be taught. I ask “or is it?” because there may be further sites which are university-affiliated “sites” (potentially “teaching forests” in the local mountains, locations much / way, way further south in Monterey County / Big Sur area) and “up the coast” (in Santa Cruz and/or San Mateo Counties) which can also be said to be UCSC affiliated (have research sponsored by them there, personnel which are located there…) and so on.
All of these, including and especially the main campus, are correctly tagged amenity=university, even as they “break the rule” that “only one object with amenity=university per university should be tagged like this.” However, I don’t think it is confusing to anybody (or any software process) what is going on: a single university has multiple locations over many sites. It’s possible to use a relation to gather these together, like a type=site or type=multipolygon relation, but this seems rare. But, it’s possible. Possibly correct (in a relational database model like OSM is), though perhaps “more richly and precisely denoted.” (Because someone took the time to carefully build all the pieces together as a relation).
Do your best; tag your best. There are many universities which have multiple sites all affiliating with a single university. Make this clear in your tagging, whether you use name=* or official_name=* as the name of the university. There are many ways to do this, and if the data are factually correct, the “OSM way” is to leave this up to “downstream parsers” (whether renderers, routers…) that coalesce these things together in a methodology that is either pleasing or correct to your eyes and tastes. We might express “one object with amenity=university per university” as a desire, but the tagging around the world doesn’t follow this guideline (and it is only that) to such an extent that it cannot be relied upon.
So, good question! But “if they are separate locations geographically, but the same university,” map them accordingly: with a similar or identical name, but on different polygons that are geographically diverse. Or, get fancy (and still correct, by being painstakingly specified) with a multipolygon or site relation. OSM affords wide varieties of specifying complex objects.
