JSFiddle - React, Tailwind, and code Playground

JavaScript

const arrayOne = [
  {
    name: 'Vasya',
    tags: [
      {name: '111'},
      {name: '222'}
    ]
  },
  {
    name: 'Petya',
    tags: [
      {name: '333'},
      {name: '444'}
    ]
  }
]

const arrayTwo = arrayOne.map((item) => {
	item.tags = item.tags.map(tag => tag.name)
  return item
})

console.log(arrayTwo)