The new name is presumably similar to the Apple Music, a provider of Apple's music streaming service. In addition to the name change, the actual overall there was no significant change between the Apple iTunes Podcast Podcast.
Quoted from 9to5Mac, the previous Cue provide leak that the company is in the stage of developing new features for Podcasts. With the change of this name, most likely Apple is preparing for this year's big announcing.
Clear that Apple is the name preferred by the consensus music, podcasts, and other content distribution service providers.
For your information, iTunes was first introduced in 1998. However, it took many years to change the name into Apple's iTunes. Especially when it is used to synchronize your iTunes music on your iPhone to a Windows or Mac computer.
Previous rumors that Apple could call the hallmark of products eliminate iTunes, downloads a song and others. However, Apple denied the report. Therefore, up to now, Apple still retains service on Apple's iTunes podcast.