When you read the input from the Second Ecumenical Council (Constantinople I) as well as the interpretation of Canon VII of the Third Ecumenical Council in the Rudder, you see that the Fathers of both councils held that the Creed was the same. The additions made in Constantinople I were not true additions, but merely a further development of those things set forth at Nicaea, as they did not change the theology or the Faith. The Fathers held that the Creed would be called the Nicene Creed, but only with the words from both Nicaea and Constantinople.
From the interepration of Canon VII as found in The Rudder:
The Councils, which accepted the Creed of the First and that of the Second as one single Creed, called only the Nicene Creed; but not so with the words of the Second Council, held in Constantinople, because they were only a development of what was concisely and implicitly contained in the Creed of the First Ec. C. or the Third Council in the present Canon expressly decreed that no one should be allowed to compose any different faith (or Creed) than that defined by the holy Fathers assembled in the city of Nicea. And divine Cyril says the same thing in his letter to the Bishop of Antioch. Besides, even the Bishop of Constantinople John, and of Rome Virgilius in writing to Eutychius of Constantinople say but this one thing. And in the fifth convention held in Florence it is written as follows: "These expositions of the Faith, or creeds of the First and Second Councils, or rather the Creed." That the Fathers of the Second Council expanded rather than added to the Creed of the First is attested by the express statements of many.
Hopefully I caught everything. I'm using a PDF version that used OCR so some of the formatting was messed up.