Having worked there during the rebranding, a big part of it was more to drive clarity around the business units (think Alphabet vs Google, only in reverse). "Comcast" refers to the overall holding company over the cable business, media business and stadium / real estate holdings.

They referred to the cable business as "Comcast Cable" for a while before rebranding it to Xfinity. The public rebranding was definitely intentional, but it wasn't the only reason behind it.