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Getting two ORCIDs assigned by two different universities is an unusual situation at this time, because only a few of us have joined ORCID as Member-Creators (the status that allows us to arrange for ORCIDs to be established for our campus constituents). In fact, a check of the ORCID list of integrators indicates that Unnamed University, where you are pursing your doctoral degree, is not working with ORCID at this time.
At some point in the future, should Unnamed University inform you that they are going to establish ORCID iDs for their graduate students, it would be a good idea to notify them that you already have an ORCID so they can use your existing iD.
More information about Managing and Preventing Duplicate ORCID iDs is available from the ORCID web site at http://orcid.org/blog/2014/01/09/managing-duplicate-iDs.