We are three licensed psychologists in New York City forming a PLLC. We find we are restricted in what we can name our PLLC...

You can use a name that is different if you register it as a "d/b/a" name with New York State.  You are restricted in the use of your name.  But, it the Secretary of State will take the name, then you can use it.  A lawyer can help you with these issues, which are not complicated.

New York law permits limited liability companies to use assumed names. There is no provision in the PLLC portion of the LLC Law that prohibits doing so. The name you assume may not be deceptive or misleading. As a general matter, assumed names should be registered to put the public on notice regarding the ownership of the assumed name; this requires filing an appropriate certificate. Some practitioners suggest that, for the avoidance of confusion or deception, business documents include both names. You may have some difficulties with simple matters like banking if you attempt to conduct business under something other than your legal name. You should consult with an attorney about this. Please feel free to call my office for advice.