diff --git a/src/datamodel_code_generator/__main__.py b/src/datamodel_code_generator/__main__.py
index 43fe4028f..84e6a9bfe 100644
--- a/src/datamodel_code_generator/__main__.py
+++ b/src/datamodel_code_generator/__main__.py
@@ -915,8 +915,13 @@ def _serialize_python_type(tp: type) -> str | None:  # noqa: PLR0911
 
 def _simple_type_name(tp: type) -> str:
     """Get a simple string representation of a type."""
+    from typing import get_origin  # noqa: PLC0415
+
     if tp is type(None):
         return "None"
+    # For generic types (e.g., dict[str, Any]), use full string representation
+    if get_origin(tp) is not None:
+        return str(tp).replace("typing.", "")
     if hasattr(tp, "__name__"):
         return tp.__name__
     return str(tp).replace("typing.", "")  # pragma: no cover
diff --git a/src/datamodel_code_generator/config.py b/src/datamodel_code_generator/config.py
index b8bc22402..25635ad25 100644
--- a/src/datamodel_code_generator/config.py
+++ b/src/datamodel_code_generator/config.py
@@ -7,7 +7,7 @@
 from pathlib import Path  # noqa: TC003 - used at runtime by Pydantic
 from typing import TYPE_CHECKING, Annotated, Any
 
-from pydantic import BaseModel, Field, WithJsonSchema
+from pydantic import BaseModel, Field
 
 from datamodel_code_generator.enums import (
     DEFAULT_SHARED_MODULE_NAME,
@@ -48,10 +48,12 @@
 CallableSchema = Callable[[str], str]
 DumpResolveReferenceAction = Callable[[Iterable[str]], str]
 DefaultPutDictSchema = DefaultPutDict[str, str]
-ExtraTemplateDataType = Annotated[
-    defaultdict[str, Annotated[dict[str, Any], Field(default_factory=dict)]],
-    WithJsonSchema({"type": "object", "x-python-type": "defaultdict[str, dict[str, Any]]"}),
-]
+if TYPE_CHECKING:
+    ExtraTemplateDataType = defaultdict[str, dict[str, Any]]
+elif is_pydantic_v2():
+    ExtraTemplateDataType = defaultdict[str, Annotated[dict[str, Any], Field(default_factory=dict)]]
+else:
+    ExtraTemplateDataType = defaultdict[str, dict[str, Any]]
 
 
 class GenerateConfig(BaseModel):
diff --git a/src/datamodel_code_generator/parser/jsonschema.py b/src/datamodel_code_generator/parser/jsonschema.py
index 4764905f0..092c18398 100644
--- a/src/datamodel_code_generator/parser/jsonschema.py
+++ b/src/datamodel_code_generator/parser/jsonschema.py
@@ -629,6 +629,12 @@ class JsonSchemaParser(Parser):
     PYTHON_TYPE_OVERRIDE_ALWAYS: ClassVar[frozenset[str]] = frozenset({
         "Callable",
         "Type",
+        # collections types that have no JSON Schema equivalent
+        "defaultdict",
+        "OrderedDict",
+        "Counter",
+        "deque",
+        "ChainMap",
     })
 
     def __init__(  # noqa: PLR0913
@@ -1399,11 +1405,16 @@ def _is_compatible_python_type(self, schema_type: str | None, python_type: str)
         return base_type in compatible
 
     def _extract_all_type_names(self, type_str: str) -> list[str]:  # noqa: PLR6301
-        """Extract all type names from a type annotation string."""
-        # Match type names: word characters starting with uppercase, not preceded by a dot
-        # This handles cases like Callable[[Iterable[str]], str]
-        pattern = r"(?<![.\w])([A-Z]\w*)"
-        return re.findall(pattern, type_str)
+        """Extract all type names from a type annotation string using AST parsing."""
+        import ast  # noqa: PLC0415
+
+        try:
+            tree = ast.parse(type_str, mode="eval")
+            return [node.id for node in ast.walk(tree) if isinstance(node, ast.Name)]
+        except SyntaxError:  # pragma: no cover
+            # Fallback to regex for non-standard type strings
+            pattern = r"(?<![.\w])([A-Za-z_]\w*)"
+            return re.findall(pattern, type_str)
 
     @staticmethod
     @lru_cache(maxsize=256)