Hi Soora thanks for posting on the community!

Because we are an online software saving in Lucidchart is done automatically any time you edit your document. You can see when your document is Saving or Saved to the right of the File menu please refer to our Get started guide for more details. 

You can edit the name of your document by clicking on the document title in the upper-right corner of the Lucidchart editor and typing in your new title. I have attached a screen recording in which I go through the process of updating a document name and I also indicate where the Saving/Saved icon can be found. 

Hope this helps!