Vue.js search functionality
One improvement would be factoring out the repeated call to this.search.toLowerCase() and storing the result in a block-scoped constant so it:

doesn't need to be calculated on every call to .includes() for each iteration of filter()
can decrease the length of each line where that value is used

That may be a small optimization but it is in line with the D.R.Y. principle
getfilteredData() {
  const lowerTerm = this.search.toLowerCase()
  return this.blogs.filter(blog =&gt;
    blog.name.toLowerCase().includes(lowerTerm) ||
    blog.category.toLowerCase().includes(lowerTerm)
  ) 
},

Additionally, it could further be simplified by using Object destructuring to eliminate the need for the identifier blog with the callback to the filter method:
getfilteredData() {
  const lowerTerm = this.search.toLowerCase()
  return this.blogs.filter({name, category} =&gt;
   name.toLowerCase().includes(lowerTerm) ||
   category.toLowerCase().includes(lowerTerm)
  ) 
},