To show the List of Related Records using Search filter in LWC, firstly we need to make a new Lightning Web Component in Vs code.
- 
Step 1 – Create a New Lightning Web Component- Press shift+ctrl+p
- Select SFDX: Create Lightning Web Component Command from the command palette.
- Now give the file name that you want.
- Select default folder :- force-app\main\default/lwc
 Now a new Component is created inside the lwc folder in your vs code. This component contains three files: Html, js, and js-meta.xml. DisplayAllRelatedRecords.html 
 <template>
 <lightning-card title="How to display the Contacts based on Account Name in LWC" custom-icon="custom:icon13">
 <div class="slds slds-p-horizontal--medium">
 <div class="slds-grid slds-wrap">
 <div class="slds-col slds-size_4-of-12 slds-m-bottom--medium">
 <lightning-Input type="search" placeholder="Search..." value={accountName} name="accountName" class="accountName" onchange={handleChangeAccName}></lightning-input>
 </div>
 <div class="slds-col slds-size_6-of-12 slds-m-top--medium" style="margin-top: 19px; margin-left: 10px;">
 <lightning-button label="Search Account Name" size="small" variant="brand" onclick={handleAccountSearch} icon-name="utility:search" icon-position="right"></lightning-button>
 </div>
 </div>
 <h2>Account Name :- <span><strong>{currentAccountName}</strong></span></h2><br/>
 <h3><strong><span style="color:brown;">{dataNotFound}</span></strong></h3><br/>
 <h2 class="slds-m-bottom--x-small" style="color:darkslateblue; font-weight:bold;">Displaying Contacts Records based on Account Name</h2>
 <table class="slds-table slds-table_cell-buffer slds-table_bordered" border="1" cellspacing="0" cellpadding="0" bordercolor="#ccc" style="border-collapse:collapse;">
 <thead>
 <tr>
 <th>First Name</th>
 <th>Last Name</th>
 <th>Phone</th>
 <th>Description</th>
 </tr>
 </thead>
 <tbody>
 <template for:each={records} for:item="conItem">
 <tr key={conItem.Id}>
 <td>{conItem.FirstName}</td>
 <td>{conItem.LastName}</td>
 <td>{conItem.Phone}</td>
 <td>{conItem.Account.Name}</td>
 </tr>
 </template>
 </tbody>
 </table>
 </div>
 <br/><br/>
 </lightning-card>
 </template>DisplayAllRelatedRecords.js import { LightningElement, track, wire } from 'lwc';
 import retrieveContactData from '@salesforce/apex/lwcAppExampleApex.retrieveContactData';
 export default class DisplayContactsOnAccountName extends LightningElement {
 @track currentName;
 @track searchName;
 handleChangeAccName(event){
 this.currentAccountName = event.target.value;
 }
 handleAccountSearch(){
 this.searchName = this.currentName;
 }
 @track records;
 @track dataNotFound;
 @wire (retrieveContactData,{keySearch:'$searchName'})
 wireRecord({data,error}){
 if(data){
 this.records = data;
 this.error = undefined;
 this.dataNotFound = '';
 if(this.records == ''){
 this.dataNotFound = 'There is no Contact found related to Account name';
 }
 }else{
 this.error = error;
 this.data=undefined;
 }
 }
 }DisplayAllRelatedRecords.js-meta.xml 
 <?xml version="1.0" encoding="UTF-8"?>
 <LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
 <apiVersion>45.0</apiVersion>
 <isExposed>true</isExposed>
 <targets>
 <target>lightning__AppPage</target>
 <target>lightning__RecordPage</target>
 <target>lightning__HomePage</target>
 <target>lightning__Tab</target>
 </targets>
 </LightningComponentBundle>To fetch data from org make an apex class in your vs code. 
- 
Step 2 – Create a New Apex Class in vscode- Press shift+ctrl+p
- Select SFDX:Create Apex Class Command from the command palette.
- Now enter the file name that you want.
- Select default folder :- force-app\main\default/classes
 Now your apex class is created inside the classes folder. Now write a query inside your Apex class to fetch the related record. fetchAllRelatedRecords.cls 
 public with sharing class fetchRelatedRecords {
 @AuraEnabled(cacheable=true)
 public static List<Contact> retrieveContact(string keySearch){
 List<Contact> mycontactList = [Select Id, FirstName, LastName, Email, Phone, Account.Name From Contact Where Account.Name=:keySearch];
 return mycontactList;
 }
 }
 In this class, we have written a query for fetching the records from contact which is in a lookup relationship with Account.OUTPUT:- 
 When the Input Box is Empty
  
 When the Related Records are available:
  
 When there is no Related Records available:
   
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