I've heard that splitting spaghetti in half before cooking them change the taste. Is it true?
No, it's not true. It will not change the way they cook. Noodle cooking times vary by what they're made out of and by thickness, not by the length of the noodles.
The kids and I seem to prefer eating shorter noodles and dodging the hassle of spinning the noodles, but when there's company over we tend to do it the classic "right" way. No difference in taste.
I can think of one way it would really change the taste, and for the better.
If you don't have a spaghetti pot and are cooking your spaghetti in a shallow pot, you first throw your spaghetti in at an angle, and a large part of them remains over water. As the lower portion cooks and gets soft, it flexes, and the upper parts slide into the water and start cooking too. In this case, half of each spaghetti rod is cooked for a longer time than the other half - if you leave them on the stove for the perfect time, one half will be slightly undercooked. Depending on how big the difference in time is, this can produce a noticeable problem in taste.
Of course, this is not a problem if you have a pot which is deep enough for the pasta to be submerged when still stiff. So your statement is true, but only under the correct assumptions.
A thought that may sound a little sciency:
You have 50 long spaghetti and 100 short spaghetti (half the length of the long ones). The short ones have twice as many spaghetti endings, so the surface of the endings of spaghetti is twice as high for the short ones.
If you believe that the endings of a spaghetti have a different taste than the central parts, then the taste of the endings becomes more influencial with shorter spaghetti.
You could try using small spherical spaghetti to get the highest possible influence of the taste of the endings.