Analog amplifier circuit
Has this amplifier a specific name?


It's a voltage controlled current sink. Vin is a demand voltage and the transistors turn on sufficiently to take a current through the load that equals \$I_{LOAD}\times R_2\$.


  I think that the resistor R1 is a resistor to limit the current, but
  how does it do that?


That is what resistors do - if you apply a voltage across tthem they restrict the current as per ohms law. R1 is probably needed to restrict the base current into T2 should the motor (say) become stalled.


  I think that R2 is a resistor to controll the voltage at the input of
  the voltage follower


Answered above.