Is there a special common name for goods sold at public events, such as T-shirts, cups, stationery, etc. being sold at conferences, concerts.
At music concerts, such items are often collectively called merch (short for merchandise). It might be appropriate to use the word by extension to refer to similar items sold at other large public gatherings, although I don't know whether merch is sufficiently widely known that the average person would know what you're talking about without explanation. Either way, the word merch should be considered slang or informal, and therefore not appropriate for formal communication.
When branded items are given away at such events, they are typically (in the United States at least) called swag collectively, which is also slang/informal.
In the UK, especially in a student context, this could be called 'stash'.
Items of clothing, usually aquired whilst at University, baring the name of a club to which the wearer belongs and usually a obscure nickname picked up in Freshers' Week. Every club or team likes to believe that they have the best stash. Highly desirable at universities like Durham, UK.
Tarquin: "Shall we do a Bailey bar crawl in our Tennis Stash?"
Rupert: "Oh golly! That would be delightful!"