The Garnishment was entered i.e. John W. Smith however the real name on the birth certificate is John E. Smith is it collectible?

It depends, Was the judgment in the correct name? Is the Social Security number correct?

Usually a typo like that would not negate a writ of execution if all the other info is correct.

However, the employer would be within it rights to refuse to execute the writ until its corrected. But that's only a delaying tactic.

As with any legal action, you have to be notified in ample time to act. It is this time that you clear up mistakes through motion to dismiss, in most states you are given 15 to 30 days to do this.