Speed Triple 955i

You need to look for the MC number, either a 1000 or 2000 and match it to what you’ve got. Depending on the model year of your bike it’ll be one of those, and you’ll find them on all the 955s.
I’ve just seen your other post about the bike not starting, must have missed that when you posted. Is that why you’re looking for another ECU?

 

You'll need a Sagem MC2000 unit. One from any of the 955cc injection bikes up to 1999 should do it, but you'll have to change the map if it's not for your exact bike. It's easy enough with TuneECU.

 

A Spark ignition engine needs: Fuel / Spark / Air supply to run properly

 

Why not post a thread to see if there’s a member near you who’s willing to have a look for you and offer a helping hand. They may have more knowledge specific to your Triumph than the garage you’re using.
It sounds like it needs a methodical check through the wiring and a Tuneecu diagnostic check.
If I were a little closer I’d help

 

That was a ridiculous suggestion by your 'shop' to install a replacement ECU because it 'might' be that with absolutely nothing to go on
First thing I would do is put the original back - you don't even know if the replacement has the correct map or even it's condition, so go back to at least what you had originally and only replace the ECU if/when you can prove it to have a problem

Is the Neutral Light on?
The ECU MUST see EITHER the Neutral Signal OR the side-stand UP - if you have no Neutral Light (even if transmission itself is in Neutral), or it's flakey, raise the side-stand and try again

When you turn on the Key, do you hear the Fuel Pump run (for about 3 secs)? (it should repeat this behaviour if you flip the Kill/Run to Kill and back to Run again)

Have you (or anyone) checked for spark or fuel?
Are the Plugs wet? Do they spark when removed and observed with engine cranking?

Have Coils And Injectors been checked for 12V supply at their connectors?

If you remove the TOP fuel hose (ONLY!!) from the pump do you get fuel pumping from it when you first turn on ignition and again when cranking the engine?

These are fundamentals that any competent shop should be able to determine.
If it's a non-Triumph shop or shade-tree, get it out of there and find someone who knows their way around Triumphs.

One of the elements I would check if you have confirmed Neutral Light and Pump running at key on and 12V supply at the coils and injectors would be the Crank Position Sensor

 

You heard it here first