Hashset in TypeScript

It exists!

mySet: Set<string> = new Set<string>();

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Set

An object {} is a key value pair dictionary is a hash set in JavaScript which TypeScript is a superset of and therefore you can use a JS object to serve in this role.

A quick version from the code you posted:

let myData = {};
for (let myObj of this.getAllData()) {
    let name = myObj.name;
    if (!myData[name]){
        myData[name] = name;
    }
}