A lot of people have posted the more technically correct reason already,
but you know I can't let a thread like this pass without commenting.

Calling out the name of a chi technique is a LOT like chanting the
incantation for a magic spell.

Rather than use Slayers examples, which would be obvious here, I'm going to
use Sailormoon examples.

The Sailor Senshi *can* use their abilities without going through the
routine of making some flashy pose and calling out the name. We've seen
Sailor Moon fling her tiara without preamble on numerous occasions, and
we've also seen Neptune and Uranus use Deep Submerge and World Shaking
without announcing them whatsoever.

Why do they often use the flashy poses and call out the attack names? Two
reasons:

1. Technically speaking, the use of a pose and a shout is a method of
focusing the energies one is summoning. It's possible to harness and
control these energies simply by DOING so, but when one is still learning,
still training, still fairly inexperienced in the use of these powers, it
helps to have a focus, something to concentrate on to channel the power.

2. Realistically speaking, it's a quirk of manga/anime. In manga, you
wouldn't neccessarily KNOW what's going on unless it's spelled out for you,
because it's difficult to illustrate the effects of a special technique in
still frames. It carries over into the anime mainly because it's what
people have come to expect, although most likely there is another, more
simple reason (ie: it's cool.)

It works the same with Ranma 1/2, Dragonball Z, etc., and the chi
techniques tossed about therein, on both counts.

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