IN THESE DAYS of fiscal crisis, budget cutbacks, layoffs, RIFS, outright firings and a reduction in the municipal services to which we all become accustomed, let me make a modest proposal which I admit, will change none of the above, but which, I insist, is long overdue. Let's change the name of the District Building to City Hall.

Why not? Washington, after all, is a city. It has all the characteristics of a city. It's deeply in debt. It elects its own mayor. It elects its own City Council (District Council?) and alas and alack, its own school board. It is in every way a city, but one. It lacks a City Hall.

There is something I noticed when I first came to Washington to cover, if all things, the District Building. Back then, the designation made sense. The city government was far different. The mayor, for one thing, was appointed and there was even some question of whether he should be called mayor or commissioner or mayor-commissioner. Mayor was chosen for reasons of civic pride, but the name had nothing to do with reality. When it came to real power, it was shared between the president and Capitol Hill. The mayor-commissioner was terrific at cutting ribbons.

But now, the city has a fairly healthy measure of home rule. It is, to a very large degree, the master of its fate and while it is true that Congress still pulls some strings and the city has not vote in Congress, it is also true that it has come a long way from the days when committee chairman on the hill ruled the city, doing for Washington what their far-away constituents thought was right and proper.

So it ought to have a City Hall. There are some, maybe, who think it ought to have a "state hall" but just the sound of it tells you that that's all wrong. (In fact, it was in deference to the statehood people that Mayor Barry withdrew a resolution to change the name of the District Building to City Hall.) State Hall sounds like a wing of the Kennedy Center or a musical by Rodgers and Hammerstein.

No, Washington should have a City Hall. It ought to have a proper one, with the name written up there in gold leaf. It ought to be a stop on the buses with the words "City Hall" up front and it ought to be a stop on the Metro, too. And when citizens get frustrated they ought to be able to say something about how they can't fight City Hall. No one, for crying out loud, ever said you can't fight the District Building. It's true, God knows, but it's unpoetic.

No matter. The District Building persists. It's a hangover, a holdover, from the old days. It sound to my ears like "colonial office" and I imagine men in pith helmets, pushing paper to and fro looking up from their desks, mopping their brows and saying something about tea. Even to this day, the District Building boasts swinging doors of the kind seen in old saloons, southern courthouses and movies about British India.

At the moment the name suggests something less than a city. It suggests that the District is, well, a district. What that is, I'm not sure, but it is something akin to a territory, an enclave, maybe a place where the hookers roam free (as in "red light district), something owned by someone else, a place that the federal government administers -- like a national park or something.

To tourists the thing must be a mystery. They see the Treasury Building, then the Commerce Building, then the District Building and they must wonder who the Secretary of the District is. To the residents, it an abomination. There it sits, like a really important building, at the head of Pennsyvania Avenue where the Avenue makes a bee-line for the Capitol. It could be a terrific City Hall. It should be a City Hall. It will be a City Hall.

For Washington is a city. It happens to be the 13th largest in the country. It is more now than just the capital. It has a basketball team, a hockey team, a soccer team, a football team, a symphony orchestra and more live theater than most cities with City Halls. It is a real town -- the place where Al Jolson and Helen Hayes were born. It's a place where people work and live and pay taxes and go to school and all it really lacks (besides decent weather) are two things: a baseball club and a City Hall. The baseball club will take some doing, but the City Hall is already there. All it needs is a new sign.