Hi Deepika,

​​​​​​​I hope you are doing well .....!!
First of all copy below code in your Org.
I have create Visualforce page and class review it and change accroding to your requirement.

Visualforce page :

<apex:page controller="testingcontroller" >
    <script type='text/javascript'>
    function callActionMethod()
    {
        alert('@@ Test123');
        var temp ="Foram Rana";
        alert('@@ temp = '+temp);
        test(temp);
    }
    </script>
    <apex:form >
        <apex:actionFunction action="{!test}" name="test" reRender="abc">
            <apex:param assignTo="{!checkVar}" name="cht" value=""/>
        </apex:actionFunction>
        <apex:commandButton onclick="callActionMethod();" value="Click me" />
    </apex:form>
    
</apex:page>

Apex Class :

public class testingcontroller {
    
    public string message{get;set;}
    public string checkVar{get;set;}
    public string name{get;set;}
    public testwrapper testwrap{get;set;}
    
    public  testingcontroller(){
        name =  '';
        checkVar = '';
        testwrap = new testwrapper();
    }
    public void test(){
        System.debug('@@@Call 78');
        message ='Hi hello'+testwrap.name;
        System.debug('@@@ checkVar = '+checkVar);
        system.debug('testwrap.name=======>'+testwrap.name);
    }
    
    public class testwrapper{
        
        public string name{get;set;}
        public testwrapper(){
            this.name ='';
        }
    }
}

Note : Make sure in apex:actionfunction there is reRender="abc" (Write as it is)

Hope this helps you.
Let me know your review.
If this helps kindly mark it as solved so that it may help others in the future.

Thanks & Regards,
Foram Rana