diff --git a/mypy/stubgen.py b/mypy/stubgen.py
index 9758e4c14973..6d5134ec9ec4 100755
--- a/mypy/stubgen.py
+++ b/mypy/stubgen.py
@@ -701,8 +701,11 @@ def visit_overloaded_func_def(self, o: OverloadedFuncDef) -> None:
                 self.clear_decorators()
 
     def visit_func_def(self, o: FuncDef) -> None:
-        if self.analyzed and self.processing_dataclass and o.info.names[o.name].plugin_generated:
-            # Skip methods generated by the @dataclass decorator
+        is_dataclass_generated = (
+            self.analyzed and self.processing_dataclass and o.info.names[o.name].plugin_generated
+        )
+        if is_dataclass_generated and o.name != "__init__":
+            # Skip methods generated by the @dataclass decorator (except for __init__)
             return
         if (
             self.is_private_name(o.name, o.fullname)
@@ -769,6 +772,12 @@ def visit_func_def(self, o: FuncDef) -> None:
             else:
                 arg = name + annotation
             args.append(arg)
+        if o.name == "__init__" and is_dataclass_generated and "**" in args:
+            # The dataclass plugin generates invalid nameless "*" and "**" arguments
+            new_name = "".join(a.split(":", 1)[0] for a in args).replace("*", "")
+            args[args.index("*")] = f"*{new_name}_"  # this name is guaranteed to be unique
+            args[args.index("**")] = f"**{new_name}__"  # same here
+
         retname = None
         if o.name != "__init__" and isinstance(o.unanalyzed_type, CallableType):
             if isinstance(get_proper_type(o.unanalyzed_type.ret_type), AnyType):
@@ -1413,6 +1422,8 @@ def is_private_name(self, name: str, fullname: str | None = None) -> bool:
             return False
         if fullname in EXTRA_EXPORTED:
             return False
+        if name == "_":
+            return False
         return name.startswith("_") and (not name.endswith("__") or name in IGNORED_DUNDERS)
 
     def is_private_member(self, fullname: str) -> bool:
diff --git a/test-data/unit/stubgen.test b/test-data/unit/stubgen.test
index 1e73df3ebb60..5fed8cd2e61f 100644
--- a/test-data/unit/stubgen.test
+++ b/test-data/unit/stubgen.test
@@ -3318,17 +3318,25 @@ def gen2() -> _Generator[_Incomplete, _Incomplete, _Incomplete]: ...
 class X(_Incomplete): ...
 class Y(_Incomplete): ...
 
-
 [case testDataclass]
 import dataclasses
 import dataclasses as dcs
-from dataclasses import dataclass
+from dataclasses import dataclass, InitVar, KW_ONLY
 from dataclasses import dataclass as dc
+from typing import ClassVar
 
 @dataclasses.dataclass
 class X:
     a: int
     b: str = "hello"
+    c: ClassVar
+    d: ClassVar = 200
+    f: list[int] = field(init=False, default_factory=list)
+    g: int = field(default=2, kw_only=True)
+    _: KW_ONLY
+    h: int = 1
+    i: InitVar[str]
+    j: InitVar = 100
     non_field = None
 
 @dcs.dataclass
@@ -3340,15 +3348,27 @@ class Z: ...
 @dc
 class W: ...
 
+@dataclass(init=False, repr=False)
+class V: ...
+
 [out]
 import dataclasses
 import dataclasses as dcs
-from dataclasses import dataclass, dataclass as dc
+from dataclasses import InitVar, KW_ONLY, dataclass, dataclass as dc
+from typing import ClassVar
 
 @dataclasses.dataclass
 class X:
     a: int
     b: str = ...
+    c: ClassVar
+    d: ClassVar = ...
+    f: list[int] = ...
+    g: int = ...
+    _: KW_ONLY
+    h: int = ...
+    i: InitVar[str]
+    j: InitVar = ...
     non_field = ...
 
 @dcs.dataclass
@@ -3357,18 +3377,51 @@ class Y: ...
 class Z: ...
 @dc
 class W: ...
+@dataclass(init=False, repr=False)
+class V: ...
 
-[case testDataclassWithKeywords]
-from dataclasses import dataclass
+[case testDataclass_semanal]
+from dataclasses import dataclass, InitVar, KW_ONLY
+from typing import ClassVar
 
-@dataclass(init=False)
-class X: ...
+@dataclass
+class X:
+    a: int
+    b: str = "hello"
+    c: ClassVar
+    d: ClassVar = 200
+    f: list[int] = field(init=False, default_factory=list)
+    g: int = field(default=2, kw_only=True)
+    _: KW_ONLY
+    h: int = 1
+    i: InitVar[str]
+    j: InitVar = 100
+    non_field = None
+
+@dataclass(init=False, repr=False, frozen=True)
+class Y: ...
 
 [out]
-from dataclasses import dataclass
+from dataclasses import InitVar, KW_ONLY, dataclass
+from typing import ClassVar
 
-@dataclass(init=False)
-class X: ...
+@dataclass
+class X:
+    a: int
+    b: str = ...
+    c: ClassVar
+    d: ClassVar = ...
+    f: list[int] = ...
+    g: int = ...
+    _: KW_ONLY
+    h: int = ...
+    i: InitVar[str]
+    j: InitVar = ...
+    non_field = ...
+    def __init__(self, a, b, f, g, *, h, i, j) -> None: ...
+
+@dataclass(init=False, repr=False, frozen=True)
+class Y: ...
 
 [case testDataclassWithExplicitGeneratedMethodsOverrides_semanal]
 from dataclasses import dataclass
@@ -3387,3 +3440,20 @@ class X:
     a: int
     def __init__(self, a: int, b: str = ...) -> None: ...
     def __post_init__(self) -> None: ...
+
+[case testDataclassInheritsFromAny_semanal]
+from dataclasses import dataclass
+import missing
+
+@dataclass
+class X(missing.Base):
+    a: int
+
+[out]
+import missing
+from dataclasses import dataclass
+
+@dataclass
+class X(missing.Base):
+    a: int
+    def __init__(self, *selfa_, a, **selfa__) -> None: ...