<apex:page standardController="Request__c" extensions="ExtensionCreatorController">
    <apex:form>
        <apex:pageBlock title="My Request Input">
            <apex:pageBlockSection title="Input Section" columns="3">
                <apex:inputField value="{!Request__c.name}"/>
                <apex:inputField id="inpMovein" value="{!Request__c.Moveindate__c}"/>
                <apex:inputField id="inpMoveout" value="{!Request__c.Moveoutdate__c}"/>
            </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>`

public class ExtensionCreatorController {

private final Request__c requ;

public ExtensionCreatorController(ApexPages.StandardController stdController) {
    this.requ = (Request__c)stdController.getRecord();
}

public InsertClone () {
    cloneRequest = requ.clone();
    cloneReqeust.name = 'EX-'+requ.name;
    cloneRequest.Moveindate__c = */here Date to be specified in Visualforce Page/*;
    cloneRequest.Moveoutdate__c = */here Date to be specified in Visualforce Page/*;
    Insert cloneRequest
}}