You can search within a text field using the SEARCH function - it will return the position in the text field at which the characters specified first appear, or 0 if the characters do not appear at all. For example,
SEARCH("Smith",[Name]) will return, for the following values of the [Name] field:
To detect the "smith" in "Naysmith" you would need to use UPPER or LOWER to convert the value of [Name] to a detectable form - both of the following will return a value of 10 for example 3 above: