===final updated==
http://plnkr.co/edit/WKRBB7?p=preview
since I use ngModel in a form, I must add name
attribue.
and my mistake is that
in you case sir if you are using *ngFor for loop then i don't think so you need index. why don't you just use x.Name. here is the modified code.
<table>
<tr *ngFor="let x of names;let i = index;">
<td>{{ i+ 1 }}</td>
<td><input [(ngModel)]="x.Name">{{x.Name}}</td>
</tr>
</table>
or can you try this
<table>
<tr *ngFor="let x of names;let i = index;">
<td>{{ i+ 1 }}</td>
<td><input [value]="x.Name" [(ngModel)]="x.Name">{{x.Name}}</td>
</tr>
</table>
It should be [ngModel]="..."
<table>
<tr *ngFor="let x of names;let i = index;">
<td>{{ i+ 1 }}</td>
<td><input [(ngModel)]="names[i].Name">{{x.Name}}</td>
</tr>
</table>