demo for https://ember-twiddle.com/

controllers.application.js

import Controller from '@ember/controller';
import { inject as service } from '@ember/service';
import { action, notifyPropertyChange, set, computed } from '@ember/object';


export default class ApplicationController extends Controller {
  appName = 'Ember Twiddle';
  @service state;
  
  @action update() {
    set(this.state, 'value', `${this.state.value}:${this.state.value}`);
    //this.state.value =  `${this.state.value}:${this.state.value}`;
   
    //notifyPropertyChange(this.state, 'value');
    notifyPropertyChange(this.state, 'name');
    //notifyPropertyChange(this, 'valueGetter');
    //notifyPropertyChange(this, 'nameGetter');
    notifyPropertyChange(this, 'nameComputed');
  }

  @computed
  get nameComputed() {
    return this.state.name;
  }

  get valueGetter() {
    return this.state.value;
  }
  get nameGetter() {
    return this.state.name;
  }
 
}

services.state.js

import Service from '@ember/service';
import { computed } from '@ember/object';

export default Service.extend({
  value: '123',
  name: computed(function(){
	  return this.value;
  }),
});

templates.application.hbs

<button type="button" {{on "click" this.update}}>
update
</button>
<br>
Direct value access:
{{this.state.value}}<br>
Direct computed access:
{{this.state.name}}<br>
Getter value access:
{{this.valueGetter}}<br>
Getter name access:
{{this.nameGetter}}<br>
Computed name access:
{{this.nameComputed}}<br>