trigger to update contact name whenever account name is updated

ContactNameUpdate.apxt

trigger ContactNameUpdate on Account (after Update) {
if(trigger.isUpdate && trigger.isAfter){
 accountNameUpdate.accountMethod(trigger.new,trigger.oldmap); }}

accountNameUpdate.apxc

public class accountNameUpdate {
public static void accountMethod(List<Account>aclist,map<id,account> oldmap){
    set<id> accountId=new set<id>();
    for(Account ac:aclist){
        account accountOld=oldmap.get(ac.id);
        if(ac.Name!=accountOld.Name){
            accountId.add(ac.Id);
        }
    }
    if(accountId.size()>0){
        map<id,account> accountmap=new map<id,account>([select id,Name,(select id,LastName from contacts) from account where id in:accountId]);
        List<contact> clist=new List<contact>();
        for(account ac:aclist){
            account accountOld=oldmap.get(ac.id);
            if(ac.Name!=accountOld.Name){
                if(accountmap.containskey(ac.id)){
                    account ac1=accountmap.get(ac.id);
                    List<contact>lstCont = ac1.contacts;
                    for(contact c:lstCont){
                        c.LastName=ac.Name;
                        clist.add(c);
                    }
                }
            }
        }
        if(!clist.isEmpty()){
            update clist;
        }
    }
}}

Based on