Is there a term for the general design used in most modern fighters?
That particular empennage design is called a “four poster” amongst the OEMs.  It’s popular because it provides both excellent longitudinal and directional stability with a minimum side profile.  As to leading edge extensions, I’ve heard of them referred to by aviation scholars as Leading Edge Extensions (LEXs) or Leading Edge Root Extensions (LERXs) they’re popular because they create a turbulent boundary layer over the inboard sections of the wing and fuselage which provides better high alpha controllability.  Canopies, such as those found on the Eurofighter Typhoon or the F-16 are sometimes called ‘blister’ or ‘bubble’ canopies because of their outraised profiles against the OML of the fuselage, providing the pilot unobstructed 360° visibility with a minimum of blind spots, so critical to air to air combat.  The serrated  or ‘dog tooth’ edges of panels are done to minimize the radar cross section around panels or skin joints.

I don’t know if there’s a particular name for such a fighter configuration, save that for that kind of a performance requirements and flight envelope, it just seems to work very well.  Similar to Bill Sweetman’s analysis in his article How the 747 Got Its Hump, given certain criteria and other demands on designing and building an airplane, this is just the best solution to the problem of designing a large twin engine fighter airplane.  It’s an open ended design so there’s no ‘right’ or ‘wrong’ answer here; it’s just certain solutions work better than others.  

They don’t always follow the mold though.  Take Lockheed’s F-22 in comparison to Northrop’s F-23 design.  The YF-22 was a stout, little chunky, conventionally styled twin fighter with stealth characteristics, while the Northrop YF-23 had a trapezoidal planform with smooth, voluptuous curved surfaces and a large pelican tail with twin all moving ruddervators.  Both aircraft excelled at what they did; a high speed low observable air superiority fighter but seemed to come to very different conclusions.  While the F-23 lost the contract, its design philoophy did not go unnoticed.  The Sukhoi design bureau seemed to draw very similar layout conclusions in the development of their Su-50 stealth fighter.  The same is true of the F-35 vs the F-32 aircraft.  LMACO’s entry was very conventional and the Boeing jet was an ungainly, unconventional delta wing design with a pelican tail, laid out largely for simplicity and ease of manufacture (which didn’t work out!).