Gonzales's carrier is called the Iliad. Fury's helicarrier is the same vessel we saw in The Avengers, the Helicarrier No. 64.
I think people take way too much notice on small details and get blinded by the big picture. Yes, there's a number 64 written in the Helicarrier seen in both Avengers 1 and 2 that we haven't seen in Gonzales' ship - which to my knowledge has been named Iliad in sources like Twitter or interviews and not specifically on the show itself - and several other visual differences between them, but what no one is taking in consideration is that the Helicarrier we see in Avengers is a CGI CONSTRUCT. That's something they cannot reasonably use here because of the lack of time and money to make it realistic so it's entirely possible they're using aerial shots of a real carrier as a replacement and we're supposed to assume it's the same one.
She's calling herself Skye. Why would they call her Daisy?
This, pretty much. They want the moment where Skye decides to start calling herself by her real name of Daisy Johnson to be a memorable one, like her undergoing Terrigenesis was in "What We Become".