The name Harpa means "harp", but is also an Icelandic female name and the name of one of the old lunar months, and the people in charge of the place want it treated grammatically as such. Thus you would not say "I am going to a concert in the Harpa" (Ég ætla á tónleika í Hörpunni), but simply "I am going to a concert in Harpa" (Ég ætla á tónleika í Hörpu).
This has offended language purists, as by leaving out the definite article the building is being spoken of as if it were a human being and not a thing. Personally, I think people should refer to it whichever way they choose.
Here you can see "her" by day and night, photos taken from almost the same spot: