Like predicate to match a whole word only
Your best bet is probably to use REGEXP, which needs some special installation prior to being usable. 

In that case, you'd use:

WHERE         
    name REGEXP 'e\w*o' 


This regular expression means: (a literal 'e') followed by (zero or more word characters) followed by (a literal 'o').

This approach won't shy away from cases like 'This hello will work'

References:


How do I use regex in a SQLite query?
Online Regular Expression tester - Regex101.com




Alternative:

If you can't install the required packages to have REGEXP available, you can probably use a user-defined function to perform the "word-by-word" LIKE check. Let's imagine it's called check_words_like(sentence, like_predicate), I'd use in the following fashion:

SELECT
    whatever
FROM
    (SELECT
        name, whatever
    FROM
        tbl
    WHERE
        name like '%e%o%'
    ) AS q1
WHERE
    check_words_like(q1.name, '%e%o%') ;


This still requires some C programming and interfacing, and might be as complicated as getting the right REGEXP package.