Assuming you have a *_ci collation (ci = case insensitive) for this column, such as utf8_general_ci, and assuming it's ok to get someone named "Govindra Raja" (where the name does not only differ on punctiation and whitespaces, but the actual name isn't exactly the same) which you then will have to manually disregard upon inspection, you don't need regexp
like 'govind%raj%'
% means match any number of any characters, so the above will match
any name starting with "govind" (upper and/or lower case letters"), followed by 0 or more characters, followed by "raj" (upper and/or lower case) followed by 0 or more characters.
However, to disregard all names that have "govind" and/or "raj" as part of the name, like "Govindra" or "Raja", you'd need to use the REGEXP operator or it's synonym RLIKE (and I don't know which or if possibly both is/are in the SQL standard).
But, if using MySQL, first note that
http://dev.mysql.com/doc/refman/5.5/en/regexp.html wrote:
Warning
The REGEXP and RLIKE operators work in byte-wise fashion, so they are not multi-byte safe and may produce unexpected results with multi-byte character sets. In addition, these operators compare characters by their byte values and accented characters may not compare as equal even if a given collation treats them as equal.
and yet, using collation utf8_general_ci does provide case insensitive regexp comparison, while utf8_bin doesn't - at least in MySQL 5.5. I have not tested against single-byte character sets.
REGEXP '[Gg]ovind[^[:alpha:]]*[Rr]aj[[:space:]]*'
matches any word starting with G or g, followed by ovind, followed by 0 or more non-alphanumeric characters, followed by R or r followed by aj, followed by 0 or more whitespaces (space, newline, tab etc).
But regexp gets no help from indexing, so you might want to use a nested query that matches 'govind%' before applying regexp
SELECT t.*
FROM (
SELECT ename, some, fields
FROM emp
WHERE ename like 'govind%'
) AS t
WHERE t.ename REGEXP '[Gg]ovind[^[:alpha:]]*[Rr]aj[[:space:]]*'
In this query, if you have a b-tree index on ename, it will be used to match against 'govind%' to retrieve rows from emp, and then the regexp will be used to match against these rows.