IKI. IT'S a name you can be proud of.

"We're the only Iki in the phone book," says Fumi Iki, beaming. "All over the country. My daughter used to be an Iki. But now she's a Weiner."

Which has very little to do with this story, except that Fumi Iki, a housewife from Silver Spring, is with the Japanese American Citizens League, one of several ethnic organizations helping with the decoration of the Smithsonian Institution's annual Christmas tree extravaganza.

The trees, representing the craft-work of various nationalities, will be on display in the Museum of History and Technology beginning Dec. 14 and through the holidays.

Iki's group is sponsoring the origami tree, an evergreen to be festooned with all sorts of figures made in the Japanese art of paper folding. (They are cheating some, though. A few of the ornaments are paper cutouts, the idea having been stolen away from the Poles.)

For several hundred years, the Japanese have been folding paper into things pleasurable to look at. Japan isn't a Christian nation, however, so the art hasn't really been translated into Christmas-speak. (Another reason for stealing some from the Poles.)

But if you put your mind to it, you will see that some objects can be made by folding paper that will look fine on your tree, such as stars and little animals.

In Japan, the crane is a symbol of good luck. If you are well-liked, says Iki, schools full of children will send you cranes to tell you what they think of you.

Some origami cranes flap their wings.

Others don't flap.

Origami went through a period here not many years ago when it was very popular. But maybe not everyone knows how to do it.

The Museum of History and Technology's bookstore carries two books on the subject, "Origami, the Art of Paper Folding" by Robert Harbin ($3.50, Harper & Row) and "Origami for the Enthusiast" by P. Montroll ( $4, Dover press).

You also will need to buy some paper. Origami paper (with instructions that are practially useless unless you read Japanese) is sold in Japanese food stores. You can also find it in the 5 & 10 or the local craft shop.

Or you can use wrapping paper, says Iki, as long as it won't crack and has a plain side, so you don't become confused while folding it. Iki cuts it down to the sizes she needs by folding it over and slicing it with a knife. Scissors create uneven edges and might leave your crane looking more like a puma.

The MHT exhibit will show traditions of all kinds, and also several different craft techniques, such as decoupage and sewing.

About a dozen persons of Lithuanian extraction are making ornaments in the Lithuanian style for the exhibit.

Lithuania, now a satellite of the Soviet Union, didn't become Christian until around the 13th Century, said Mary Brienzius Williams, an account representative with Professional Travel Management, Inc. So they still think very much of wheat.

Strange as that may sound, wheat is an important part of Christmas in Lithuania, especially since Lithuanians don't think much of cutting down trees.

"Bringing wheat into the home during the Christmas solstice," said Williams, "was an act of sympathetic magic. The wheat stalks represented the sun's rays."

Lithuanian ornaments are made of the shafts of straw, in geometric patterns, mostly. Triangles are the fundamental form and are combined to make intricate stars and mobiles.

The shafts are connected with a heavy thread, the triangles joined at the corners. Sometimes you can use a needle on short sections. On longer sections, however, Williams uses a piece of florist's wire.

The problem, in Washington, is where to get the wheat. Drive to Nebraska?

Williams says you can buy or order it from a florist.

Another problem with wheat shafts is they crack. So Williams suggests that beginners start out on plastic or paper soda straws, though there is little magical about the ones with the little red lines in them. Also avoid the creased ones that bend for persons who have to drink while lying on their back. c

Unfortunately, there aren't many books on the subject of making Lithuanian Christmas ornaments. But in Chicago, where the largest Lithuanian populations outside Lithuania lives, the Balzekas Museum publishes a pamplet.

You can write the museum at 4012 Archer Ave., Chicago, Ill. 60632.

Or you can just enjoy the ones others have made at the Museum of History and Technology.