I've created a smart capture form for lead generation. The form will be added to the website and I wanted to customize the submission message in order to add the name filled in the form. I've tried several ampscript tests but I'm not able to get the resulat that I want ! 
Many thanks for your help !
There may a complex programmatic approach to achieve your requirement. However, I am sharing my point of view.
First I will cover the best/easiest solution; later ll exlain why your requirement is NOT possible to achieve out of the box.
Alternate Solution: Just use the second option of 'URL Redirect' use a separate ThankYou Cloud Page as below. And make use of the RequestParameter() in your ThankYou page to display any field from your form.
Below info if just in case you want to know more,
Smart Capture default JS = https://cloudpages.mc-content.com/CloudPages/lib/smartcapture-formjs.js
Basically the SmartCapture form gets submitted using AJAX method and NOT using FORM submit method; hence the page does NOT get Refreshed [instead the Payload] gets submitted asynchronously behind the scene]
Hence your thank you message, is preloaded in payload as you can see under HTML editor. 
