the definition of a hurricane (i.e naming what that is forming) is concentric gales around the center (and being warm core)
you can get that in the tropics from a relatively shallow baro reading at the center (e.g 995, where the normal barometer reading around it might be say 1015)
what's its over land, the windspeed needs to drop below hurricane force (average) to be renamed a tropical depression
once it looses its hurricane rainbands wrapped around the center, then it becomes ex tropical (and then transforms into a mid lattitude depression (where rain band arms (one of which is stalled over Houston (which has a problem))