Hy, can someone tell me what this hose is called?

That's the turbo air in hose ( the big one). I believe the little one is the pcv hose.

Turbo pressure does not go through those hoses.

If this is a tdi, the usual cause for lack of power, is due to the turbo vanes not moving. Which causes no boost.

Have someone check the vanes for correct operation (vacuum pod, vacuum solenoid & hoses).

A bad Maf sensor can also cause lack of power, so have them check that too.

Thomas

I attached the hose diagrams from the service manual.

Those images are for the 1.8T gas engine. The engine in question
is a TDi Diesel (if you look at the image the customer posted you
should be able to tell.)

The hoses in the pictures are not even labeled.

Thomas

A couple pictures attached.

First one is the "suction side" (no boost pressure).

Second is the "pressure side)

Tell me the part number and I will tell you the part name dealer part
number.

Vacuum & pressure leaks are best found with a smoke machine. Take
the car to someone who can pressure test the system.

Thomas

They are labeled it is just the screen shots make it so hard to see the numbers next to the parts.
The fact that I posted the wrong diagrams is my fault as I did believe I had the correct diagrams.
In or service manual the only turbo is the turbo diesel.

Your very welcome ans as you can see we ghave a lot of people who want to help.