The network wanted to make the change to bring in younger viewers.  Starting in January of 2016 their name will be known as Freeform. Here is some info from Entertaintment Weekly:

Starting in January, ABC Family will be known as Freeform.

The switch is part of an effort to attract more of what the network calls “Becomers,” viewers between the ages of 14 and 34.

The network’s programming style — led by shows like Pretty Little Liars, The Fosters, and Young and Hungry — will essentially remain the the same.

In researching a new name, Freeform accomplishes a few different goals the network was striving to hit. The name suggested content that could be viewed on different screens and shared and discussed in multiple ways (ABC Family viewers are big on social media). That viewers no longer just consume content but create it as well was a consideration too. And Freeform, ultimately, was a name that simply generated a positve emotion. “We wanted an emotional response to a name that made people happy,” Ascheim said. “We got an overwhelmingly positive response. Freeform sounds like fun.”

Source: Entertainment Weekly