As long as the original field is consistent, you should be able to do this with a pattern match. If you have a field called NAME, then something like this would work:

Create a pattern matching activity. Generate a new token called FIRST, with %(NAME) for the input and ^\S+ for the pattern. Then create another new token called LAST with %(NAME) as the input and \S+$ as the pattern. Finally, add an Assign Token Values activity, where you can make a new token with %(FIRST).%(LAST) using the tokens from your pattern match.

Just a warning though... names are notoriously difficult to work with because there's lots of ways they can vary... (Middle initials, hyphenated names, people who entered the data as Last,First, etc...) What I gave you above will only grab the "first name" from the start of the Name field to the first whitespace character, and the "last name" will be from the last whitespace character to the end of the string. Depending on your input, these could be empty matches, and they would ignore any words in the middle of an expression. A few examples:

"Test Name" >> "Test.Name"

" This Has a Space at the start" >> ".start"

"Neal Mac Adams" >> "Neal.Adams"