Add minlength="2" (see minlength support table) to restrict the minimum length to 2 chars and remove the space between + and ( as spaces are meaningful in regex patterns.
<form action="/action_page.php">
Full Name:
<input type="text" name="full_name" minlength="2"
pattern="^[a-zA-Z]+(\s+[a-zA-Z]+)*$"
title="Enter your Full name( First name, Last name)">
<input type="submit">
</form>
Note that you may also remove ^ and $ in the pattern and use
pattern="[a-zA-Z]+(\s+[a-zA-Z]+)*"
because HTML5 engine will put the pattern in between ^(?: and )$, thus ensuring an entire string match.
If browsers that do not support minlength should be supported, use a lookahead check at the start:
pattern="(?=.{2})[a-zA-Z]+(\s+[a-zA-Z]+)*"
The (?=.{2}) will require 2 chars immediately after start of the string is asserted (mind pattern="(?=.{2})[a-zA-Z]+(\s+[a-zA-Z]+)*" will be translated into /^(?:(?=.{2})[a-zA-Z]+(\s+[a-zA-Z]+)*)$/ regex, with or without u modifier depending on the browser).