The turnover in New York City apartments is possibly greater now than at any time during the 1980's, as more people seek to share living costs in the aftermath of last October's stock-market collapse.

''With the economy the way it is and everyone tight on dollars, we're finding more people willing to share - three people sharing one-bedrooms,'' said Mark Montalbano, vice president of the rental division at J. I. Sopher. ''Some people who wanted to rent an apartment alone for $1,300 or $1,500 now want to share a two-bedroom for $1,800. Any time you get involved in a roommate situation, there's a greater chance that the apartment will be turned over or vacated.''

The law in New York allows landlords to put as many names on a lease as they wish, but as a rule there are usually only one or two names per lease, or three if the apartment is large. In addition, where there is only one tenant named on the lease, the ''roommate law'' allows one ''additional unrelated occupant'' without the landlord's consent. When the prime tenant moves out, though, the roommate also must leave.

Some managers and owners set their own guidelines within the law. For instance, Charles H. Greenthal, a real estate concern that oversees 100 rental buildings in Manhattan and Queens, will put two or three names on a lease. But if one of the tenants moves out, the name is taken off the lease and the replacement is treated as an ''additional occupant'' without an opportunity to sign.

''We don't want people using the building as a hotel,'' said Tim Fine, a vice president at Greenthal. ''If three women or three gentlemen are sharing, and one moves out after six months, you would have people constantly shuffling in and out, and the lease would be too difficult to keep track of.''

SUCH policies can frustrate young adults searching for apartment security. ''Getting your name on a lease is a plus,'' said Ms. Jimenz, who hopes to add her name to the lease in August. ''It's power in New York City. Owning something for a time is what a lease is all about. They can't throw you out.'' For landlords, deciding whether to put just one person on the lease or include everyone in the apartment is difficult because both ways involve trade-offs. According to Gary M. Rosenberg, a lawyer who represents building owners, if a landlord decides to go with ''multiple names on a lease,'' there is a better chance the rental income will continue uninterrupted. But at the same time, vacancy increases will often be sacrificed, and the apartment itself will age more quickly. ''Clearly, if you have a one-bedroom apartment with three people, the wear and tear will accelerate,'' Mr. Rosenberg said. ''The refrigerator will open and close three times as often. There's a cost factor.''

On the other hand, the landlord who opts for only one person on the lease will get the vacancy increase allowed for rent-stabilized apartments on each change of tenancy. And the apartment will look newer longer. But ''if you have a single tenant on a lease, it is much more likely that you will be stuck for rent upon a vacancy,'' Mr. Rosenberg said.