Why is it that in OWL, we don't use unique name assumption? Does it not more complicate things because if two things have different name, is it not ok for it to be different?
OWL does not assume unique names. The reason should be obvious. If Esperanza, who lives in Argentina, and Théophile, who lives in France, both want to describe Barack Obama, they'll need an identifier for him. Esperanza decides that the obvious identifier for the current US president is http://dbpedia.org/resource/Barack_Obama, while Théophile thinks that an identifier from government data is more appropriate, such as http://data-gov.tw.rpi.edu/vocab/Barack_Obama. If unique name was assumed, then these two identifiers would necessarily identify two different things.
There are plenty of things in the universe that are known by many names. That's why the phrase "a.k.a." exists. That's why owl:sameAs exists. UNA has advantages for the consumers of data, but it has huge drawbacks for publishers. The Web, and therefore the Semantic Web, is based on the principle that you don't have to coordinate to publish things. You never have to agree on a specific identifier to say something about the world.