I have a fixed set of people who give me some feedbacks.

I have a fixed set of people who give me some feedbacks.

Within the form, can my people select there name from a drop box , and fill the form?

post submission, based on the name selected, they should receive an completed form via SMS and email.

Example: Mr John is filling the form, then he should be able to select his name from the drop box. and post submission, John should receive the SMS Notification and email notification.

Hello,

Within the form, can my people select their name from a dropbox, and fill the form?

You can use the Autocomplete widget to add the fixed set of names OR you can add the fixed set of names in a regular drop-down form field.

Post submission, based on the name selected, they should receive a completed form via SMS and email.

Ensure that there is an email field on the form so that the persons on this fixed set can enter their emails. Once that is done, if you have set up an autoresponder email in the form, they can get an email after the form is submitted.

Here is a related guide for reference: Setting-up-an-Autoresponder-Email 

There is, however, no direct option to send the submission as an SMS. You can integrate JotForm with Zapier and send SMS notifications to your users: https://zapier.com/zapbook/jotform/sms 

You could also check out the workaround suggested by my colleague on this link: https://www.jotform.com/answers/1434385-How-do-I-send-SMS-text-messages 

Do review and let us know if you have any further questions.