Angular Material mat-table is not showing updated data from data source

Reference to dataSource remains the same so that material doesn't know that your source changed.

Try

this.dataSource = [...this.data];

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Or use BehaviorSubject like:

dataSource = new BehaviorSubject([]);

onAdd($event){
  this.data.push({name: this.currentText});
  console.log(this.data);
  this.dataSource.next(this.data);
}

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Instead of push use concat to let table know that you modified the object

   this.data = this.data.concat([{name: this.currentText}]);