Question on rationale behind doubled "Int. Math. Res. Not. IMRN" journal name
This is just speculation, but the reason could be because of the slightly complicated history of the IMRN journal. 

Throughout you should remember that MathSciNet grew out of what originally was a print publication called Mathematical Reviews. It was extremely important that they have a uniform house style for referring to journals. 

Originally there was a journal called International Mathematics Research Notices published by Duke Univ. Press from 1991-2001. On MathSciNet its abbreviation was Internat. Math. Res. Notices. When the journal moved publishers to Hindawi in 2002, the abbreviation became Int. Math. Res. Not. on MathSciNet. In 2005 Hindawi started a new journal called International Mathematics Research Papers, which was indexed by MathSciNet under the abbreviation IMRP Int. Math. Res. Pap. 

In 2006/7, the two journals were both transferred to Oxford Univ. Press. There was some relationship between the two journals (I remember seeing it in an old author submission guideline) and the two are treated as sort of a pair. Probably in an effort to clearly distinguish the two journals, either OUP or MathSciNet decided to list the two journals as, respectively, International Mathematics Research Notices. IMRN and International Mathematics Research Papers. IMRP with abbreviations Int. Math. Res. Not. IMRN and Int. Math. Res. Pap. IMRP. 

In 2009 or thereabouts, OUP merged IMRP into IMRN. 

I would surmise that the "duplication" appeared in an effort to add some redundancy for better disambiguation of two journals with extremely similar titles. Now it survives as a vestigial testament to the journal's history.