The cosmos was a name that bought. There is NO link from the old team to the new other than someone paid for it like a vanity domain name.
No simpleton...that was not what was bought. What was bought was the legal entity itself, the same one that has been kept active since the mid 70's, including all assets and holdings of the company. In 2010 Kemsley acquired ownership of the New York Cosmos (not just a name or trademark), similar to an investor buying a majority stake in an existing business. The entity itself has been kept alive ever since 1985, it never folded, disolved or ceased to exist. Pepe continued to run the New York Cosmos until 2010 and paid corporate taxes, and used the New York Cosmos entity to further some of his own camps and such. The only thing that hasn't been present and continuously ongoing this whole time, is the professional soccer team itself because Pepe could afford to form a professional team alone. The New York Cosmos have been around and active the entire time, but a team to play professionally has been dormant.
In 2013, O'Brien and Sela investors bought out Kelmsey for control of the New York Cosmos and organized a professional team to take the field for the first time in almost 30 years.
Its the same ORGANIZATION!! Just now with different owner, and as such all the rights and history of that organization remains the same. That is why they can call themselves the same New York Cosmos, run around with all the trophies from the last time they were active, and be recognized by FIFA and the world as the New York Cosmos.
The only people saying they are not the same are people with fantastical or romanticized views about a very small period of existence of the team 77-82 when they were at their best. To them that time can not be duplicated and should be buried in the past forever. (or just plain haters). They are offended anyone would try and bring back the Cosmos because to them they died forever, too bad facts don't support that viewpoint.