What is the name of the groove down the middle of an anther?
I think what you are looking for is the connective. Anthers are usually two-lobed and connected by a band of sterile tissue that also connects the anther with the filament - therefore the name, I guess (see Wikipedia article for stamen). It says


  Most commonly anthers are two-lobed and are attached to the filament either at the base or in the middle area of the anther. The sterile tissue between the lobes is called the connective.


Each anther lobe usually consists of two pollen sacs (see Wikipedia article for microsporangia). It says:


  Each anther lobe develops two pollen sacs. Thus, a two-lobed anther develops four pollen sacs situated at four corners of the anther.


And further (accentuation by me)


  The cells of endothecium possess fibrous thickenings. They remain thin-walled and constitute stomium (line of dehiscence) in the shallow groove in between the two microsporangia of the anther lobe.


This groove frequently is called by its orientation, i.e. longitudinal groove, even though I do not think this really is a well-defined technical term (but do a quick Google search for "longitudinal groove" anther and you will find several biology books using the term, e.g. this).