Bebe Neuwirth is so unlike Cheers' tightly wound psychiatrist Dr. Lilith Sternin-Crane, the role which won her an Emmy this year, that most people don't recognize her in real life. That's fine with her ''I aspire not to be recognized,'' Neuwirth says. When director Peter Weir's film Green Card opens this week, the Princeton, N.J.-born, bicoastal actress, who is married to actor-director Paul Dorman, may get her wish again. In her first big movie part, she plays a rich, rebellious hellion unlike either the actress or the shrink. As Andie MacDowell's on-screen best friend, Neuwirth returns to the sort of tough-girl part she regularly sang and danced on Broadway and which earned her a 1986 Tony for Sweet Charity. The 30-something Neuwirth says she means to keep losing herself in roles in all three media and have fun doing it, but in Green Card she may have had too much fun with MacDowell (''I didn't want to stop being her best friend'' when filming ended) and steamy French star Gerard Depardieu. ''I was so busy having a good time I lost track of my work,'' she says. ''That will either be a really good thing or a very, very bad thing.''