Its own label. Its own name.[nitpick mode on]
That syntax is something that drives me crazy, and it's all over Wikipedia.
"Would have" is a phrase that applies only if something was considered but not implemented. If it actually happened, the correct way to state it is by use of the past tense.
Clear Channel had news under their own label after 9/11.
or
Clear Channel began a news operation under their own name after 9/11.
[nitpick mode off]