Component HTML:

<template>            
    <lightning-card title = "Search Accounts" icon-name = "custom:custom63">       
        <div class = "slds-m-around_medium"> 
                  <lightning-input type = "search" onchange = {handleKeyChange} class = "slds-m-bottom_small" label = "Search" > 
            </lightning-input>       
            <template if:true = {accounts}>                       
                <div style="height: 300px;">       
                    <lightning-datatable key-field="Id" 
                                         data={accounts} 
                                         columns={columns} 
                                         hide-checkbox-column="true" 
                                         show-row-number-column="true"> 
                    </lightning-datatable>       
                </div>
            </template>           
            <template if:true = {error}>       
                {error}>                       
            </template>       
        </div>       
    </lightning-card>       
</template>  

Component JAVASCRIPT:

import { LightningElement, track } from 'lwc';  
import fetchAccounts from '@salesforce/apex/AccountController.fetchAccounts';  
 
const columns = [  
    { label: 'Id', fieldName: 'Id' }, 
    { label: 'Name', fieldName: 'Name' }, 
    { label: 'Industry', fieldName: 'Industry' }, 
];  
 
export default class accountSearchLWC extends LightningElement {  
 
    @track accounts; 
    @track error; 
    @track columns = columns; 
 
    handleKeyChange( event ) { 
         
        const searchKey = event.target.value; 
 
        if ( searchKey ) { 
 
            fetchAccounts( { searchKey } )   
            .then(result => { 
 
                this.accounts = result; 
 
            }) 
            .catch(error => { 
 
                this.error = error; 
 
            }); 
 
        } else 
        this.accounts = undefined; 
 
    } 
 
}  

Apex Class:

public with sharing class AccountController {  
 
    @AuraEnabled( cacheable = true ) 
    public static List< Account > fetchAccounts( String searchKey ) { 
     
        String strKey = '%' + searchKey + '%'; 
        return [ SELECT Id, Name, Industry FROM Account WHERE Name LIKE: strKey LIMIT 10 ]; 
         
    } 
     
}  

Output: