The Sony Bavaria KDL TV's are fairly old models. The letter K has been used as a prefix for Sony TVs for at least 20 years.
The two letters after the K (the D and L in your case) have changed over the years to designate what type of TV it is - CRT, Projection, Plasma, OLED, LCD, etc. In your case, the KDL prefix simply indicates the TV is an LCD type model.
What you need to input is part of the actual model/device number
It should be in the format of KDL-40R450B or KDL-40R453B or KDL- 55EX645
When pairing the 360 with the TV you should try inputting the first 4 characters after the screen size.
Examples using the above three models.
For the KDL-40R450B you would input R450 (the 4 characters after the screen size which was 40)
For the KDL-40R453B you would input R453 (the 4 characters after the screen size which was 40)
For the KDL- 55EX645 you would input EX64 (the 4 characters after the screen size which was 55)
If that doesn't work then you should try the key testing method.
Audio & Video > Pair remote with devices > TV devices
Don't just accept the first one that appears to work. Try a few more as (like the older V6 and Tivo boxes) there are often 3 or 4 that will work, some more fully than others
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