Method type restrictions for StringConcatFactory.makeConcat are about return type & maximum number of arguments. This would mean 0 & 1 argument method types are valid. This calls for the definition for concatenation with 0 & 1 params.
Specifically
StringConcatFactory.makeConcat(lookup(),
                                                        "name",
                                                       MethodType.methodType(String.class));
and
StringConcatFactory.makeConcat(lookup(),
                                                        "name",
                                                       MethodType.methodType(String.class, String.class));

Note: Though the API refers to JLS 15.18.1 "String Concatenation Operator +", the JLS section only talk about concatenation of 2 arguments.