Cannot access Inputs from my controller/constructor

You must implement OnChanges, see below:

import {Component, bootstrap, Input, OnChanges} from '@angular/core';
import DataService from './data-service';

@Component({
    selector: 'app-cmp',
    template: `{{data.firstName}} {{data.lastName}} {{name}}`
})
export default class NamesComponent implements OnChanges {
  @Input() data;
  name: string;
  constructor(dataService: DataService) {
    this.name = dataService.concatNames("a", "b");
    console.log(this.data); // undefined here
  }
  ngOnChanges() {
    console.log(this.data); // object here
  }
}

Because the Input property isn't initialized until view is set up. According to the docs, you can access your data in ngOnInit method.

import {Component, bootstrap, Input, OnInit} from '@angular/core';
import DataService from './data-service';

@Component({
    selector: 'app-cmp',
    template: `{{data.firstName}} {{data.lastName}} {{name}}`
})
export default class NamesComponent implements OnInit {
  @Input() data;
  name: string;
  constructor(dataService: DataService) {
    this.name = dataService.concatNames("a", "b");
    console.log(this.data); // undefined here
  }
  ngOnInit() {
    console.log(this.data); // object here
  }
}