My copies of the series episodes with the exception of the first ALL have the Jessica Jones logo as described in your second image.
In December 2014, the official title was revealed to be Marvel's A.K.A. Jessica Jones, but that was shortened to Marvel's Jessica Jones in June 2015.
A version of the series was originally in development by [Melissa] Rosenberg for ABC in 2010, which was eventually passed on. By late 2013, Rosenberg reworked the series, when it re-entered development for Netflix as A.K.A. Jessica Jones
The first episode, as you said, has the original name of the series; A.K.A. Jessica Jones. I cannot find any information as to why this was not changed after the fact but it's possible that, as the first episode, it was already in the can and no-one thought it necessary.
Subsequently produced episodes would have the final name.
You might note that all the episode names start with AKA.