Yes, it's possible, but it's application dependent.  The RFC allows for any number of attribute=value parameters, and provides some example ideas as well.  Thunderbird does respect a filename=<file.ext> parameter but Firefox does not.  Try testing it yourself.  Here is the stackoverflow logo in svg format from wikimedia commons base64-encoded and formatted in the data URL scheme:

data:image/svg+xml;base64,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

You can copy/paste that into your address bar and you should see stackoverflow's logo rendered.  Try and save it and, in Firefox, it will default to Untitled.svg.

Now, add a filename parameter:

data:image/svg+xml; filename=Stack_Overflow_icon.svg; base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAxMjAgMTIwIj48c3R5bGU+LnN0MHtmaWxsOiNiY2JiYmJ9LnN0MXtmaWxsOiNmNDgwMjN9PC9zdHlsZT48cGF0aCBjbGFzcz0ic3QwIiBkPSJNODQuNCA5My44VjcwLjZoNy43djMwLjlIMjIuNlY3MC42aDcuN3YyMy4yeiIvPjxwYXRoIGNsYXNzPSJzdDEiIGQ9Ik0zOC44IDY4LjRsMzcuOCA3LjkgMS42LTcuNi0zNy44LTcuOS0xLjYgNy42em01LTE4bDM1IDE2LjMgMy4yLTctMzUtMTYuNC0zLjIgNy4xem05LjctMTcuMmwyOS43IDI0LjcgNC45LTUuOS0yOS43LTI0LjctNC45IDUuOXptMTkuMi0xOC4zbC02LjIgNC42IDIzIDMxIDYuMi00LjYtMjMtMzF6TTM4IDg2aDM4LjZ2LTcuN0gzOFY4NnoiLz48L3N2Zz4=

I added spaces too to make it easier to read, which are also valid.  Copy/paste that to your address bar and, in Firefox at least, it will still try to save it as Untitled.svg.

Finally, in Thunderbird, start composing a new HTML message and go to Insert > HTML and give it an img tag with that data: URL for the src attribute:

<img src="data:image/svg+xml; filename=Stack_Overflow_icon.svg; base64,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" />

After you click insert you should see the lovely stackoverflow logo.  Now, just save the message in your Drafts and then head over to it so you can view it as a written e-mail. Right-click on the stackoverflow logo and Save Image as... and what do you know? it will default to saving it as Stack_Overflow_icon.svg for you.