As per the ERC-721 contract on OpenZeppelin, you can create a token with this constructor:
constructor(string _name, string _symbol) public {}
Does the "_symbol" have to be unique across the blockchain? If yes, then how can one find a unique public _symbol? Is there a public register maintained?
If it doesn't have to be unique, then a duplication of a contract with the same name and symbol, won't it confuse the people searching for your _symbol?