select * from table1 where
table1.name
REGEXP '^1.1$'
makes sure that only 1.1 is allowed (but also 1X1 or 111 because the dot matches any character - if you want to match a literal dot, use ^1\.1$).
Of course, now there's the question why you'd want to use a regex at all since it's just a literal string you're matching, not a variable pattern.
Your regex failed because you were using start-/end-of-word anchors that match between alphanumeric characters and non-alphanumerics (or start/end of string), and since [[:>:]] matches between 1 and ., the regex matched 1.1.1 at least partially.