The Transportation Department has unveiled plans to transform its quarter-century-old National Driver Register into a computer-assisted "rapid response system" that by the end of the decade will help target bad drivers instantly when they apply for a new driver's license in a different state.

But because of privacy concerns about creating a new national information center -- and the Reagan administration's general tilt toward turning more responsibility over to the states -- the new register will simply be a streamlined version of the old one. It will link the driving-license record systems of the 50 states and the District but provide only minimal identifying information.

Clayton Hatch, who is in charge of the register, said, "Because we are making the file more accessible, to offset the privacy considerations we have decided not to be the custodians of this information." Instead the states will continue to hang onto it.

The register now stores reports of suspended and revoked driver's licenses in a central file and mails that information to states at their request. But the process often takes a week or two, far too long for the many states that issue driver's licenses while a person waits.

As a result, a person whose license has been suspended in one state now can apply for a new license in another state and drive away long before the information on his record reaches the licensing authorities.

The Transportation Department also has had trouble keeping information in the current national register up to date.

But under proposals for the new register, the department eventually will be linked to computers in all the states. The register will keep on file the names of those who have been denied a license or had their driving privileges revoked, those involved in fatal accidents and those who have given false information to licensing officials.

No details will be kept in the national file, however; the requesting state will have to retrieve that information from the state that took action against the driver.

The new system will be phased in over the next five years, beginning with a pilot test program involving four states, soon to be chosen. Transportation officials expect all states to be converted to the new system by October 1989.