A limited liability company formed or existing under or subject to this act that is licensed or is to be licensed as a nursing home under article 17 of the public health code, 1978 PA 368, MCL 333.20101 to 333.22260, may use the term “health center” or “health care center” or a term conveying a meaning substantially similar to those terms, or the term “rehabilitation center”, as long as those terms do not conflict with the terms prohibited by section 21712 of the public health code, 1978 PA 368, MCL 333.21712.