You can split the string up by words first, like this:
var result = "Ben Stiller".Split(new string[] { " " }, StringSplitOptions.RemoveEmptyEntries)
.Any(x => x.StartsWith("Sti"));
Of course you could write this as you're own extension method, like this:
public static bool AnyWordStartsWith(this string input, string test)
{
return input.Split(new string[] { " " }, StringSplitOptions.RemoveEmptyEntries)
.Any(x => x.StartsWith(test));
}