Add property to object when it's not null

You could use Object.assign in combination with the ternary operator:

let data = Object.assign({},
  first === null ? null : {first},
  ...
);

This works because Object.assign will skip over null parameters.

If you are sure that the property value is not going to be "falsy", then it would be bit shorter to write:

let data = Object.assign({},
  first && {first},
  ...
);

Assuming the object is going to be stringified at some point, since stringification ignores undefined values, you could also try

let data = {
  first: first === null ? undefined : first,
  ...
}

Depending on the JS version you are using, you can use the spread operator ...

const getData = data => ({
  ...data.first  && { 'Custom First Prop Name': data.first },
  ...data.second && { 'Custom Second Prop Name': data.second },
  ...data.third  && { third: data.third },
  ...data.fourth && { fourth: data.fourth },
});

Non-inline solution

If you don't need to add the value inline, it is pretty straightforward and clean to write your assignment like this.

const val1 = 1
const val2
const data = {}

val1 && (data.a = val1) // 1
val2 && (data.b = val2) // Not added
// data = { a : 1 }

NOTE: This will not work if the value is falsey