Never heard of ereg, but I'd guess that it will match on substrings.
In that case, you want to include anchors on either end of your regexp so as to force a match on the whole string:
"^[a-zA-Z]+$"
Also, you could simplify your function to read
return ereg("^[a-zA-Z]+$", $myString);
because the if to return true or false from what's already a boolean is redundant.
Alternatively, you could match on any character that's not a letter, and return the complement of the result:
return !ereg("[^a-zA-Z]", $myString);
Note the ^ at the beginning of the character set, which inverts it. Also note that you no longer need the + after it, as a single "bad" character will cause a match.
Finally... this advice is for Java because you have a Java tag on your question. But the $ in $myString makes it look like you're dealing with, maybe Perl or PHP? Some clarification might help.
ctype_alpha($myString);