When you use the HTTP GET method to submit the form, and the produced URL is allowed to be crawled/indexed, then it can matter for SEO in the way that it’s just another part of your URL.
<input type="text" name="e" /> might produce an URL like:
<input type="text" name="email" /> might produce an URL like:
If or to which extent such signals in the URL may matter for SEO is discussed in various questions here.
One thing is sure: If these URLs are indexed and a user is searching for "email", many search engines (including Google) will highlight occurences of this term in the search result snippet. This may lead to more clicks, even more so if the term in question is not also part of the page title/description.