What is the name of this vintage helicopter trainer?
It is a Flettner Bo102 Helitrainer. There were 18 of these produced which were used by six countries.


Source: Airus Helicopter History

Here are some more pictures

It is also known as the Bölkow Bo 102 (Wikipedia).

From Aviastar.org:


  Rolled out in 1959, this Helicopter Trainer was powered by a 40hp ILO piston engine and had a twenty-one foot counterbalanced fibreglass rotor blade. In all eighteen of these HeliTrainers were built operating throughout Europe, training military helicopter pilots. Although unable to fly, they were ideal for the teaching of hovering techniques and were replaced by dual trainer helicopters.
  
  The Bo-102 Helitrainer, powered by a 40hp Hirth engine driving a simple one-bladed rotor with a counterweight, was developed in land and water based versions, both of which were semi-captive. This feature allowed the helicopter to rise to a height of 0.6m, turn around a vertical axis and dip at up to 6� but prevented it from flying outside these limits.