Be it electronic transformer, electronic ballast, MR16, or a host of other items where the old name has migrated to new products, giving the name used by the advertisers is the right way, and if MR16 will find the part, then that is the right word to use in google even it not the right name.
Today it is very hard to find true LED MR16 lamps, as most LED lamps don't have the reflector.
As to move to LED there are 4 options to allow the move.
1) Original powered from a toroidal transformer then simply swap. Being careful to select non DC lamps, and most are not DC anyway.
2) Original powered from an electronic transformer with range 50 - 200 VA swap the power pack for either a toroidal transformer, or an electronic transformer marked 0 - 50 VA or use a DC power pack often called incorrectly a driver, a driver should be current control, but it seems 12 volt voltage regulated devices also called drivers. Best option electric wise is the toroidal transformer, as many lamps marked 50 Hz.
3) Swap to GU10 fittings, and do away with the transformer.
4) Get special GU5.3 230 volt bulbs, not recommended as too easy fit wrong ones latter, and the fitting may not be insulated to the correct amount for 230 volt use.
This link shows likely the best option but depends if it will physical fit.
also
this electronic version will work it can go down to zero output,
the output is not likely to be 50 Hz so there is a slim chance it could with LED lamps become a small transmitter, so should be placed close to the bulbs, there is normally a maximum cable length. It is supplied with 300 mm of 12 volt lead, should not really exceed that length although think it is unlikely to cause a problem.
Since you say spot like track which may not be insulated well enough for 230 volt, I would swap holder which is damaged and if not already a toroidal transformer then fit either toroidal transformer or the electronic one shown. The electronic one can be dimmed.