diff --git a/myst_nb/core/config.py b/myst_nb/core/config.py
index d90e85ab..d3b11080 100644
--- a/myst_nb/core/config.py
+++ b/myst_nb/core/config.py
@@ -188,6 +188,14 @@ def __post_init__(self):
             "sections": (Section.global_lvl, Section.execute),
         },
     )
+    eval_name_regex: str = dc.field(
+        default=r"^[a-zA-Z_][a-zA-Z0-9_]*$",
+        metadata={
+            "validator": instance_of(str),
+            "help": "Regex that matches permitted values of eval expressions",
+            "sections": (Section.global_lvl, Section.file_lvl, Section.execute),
+        },
+    )
     execution_mode: Literal["off", "force", "auto", "cache", "inline"] = dc.field(
         default="auto",
         metadata={
diff --git a/myst_nb/core/execute/base.py b/myst_nb/core/execute/base.py
index edcfd03d..befb6d29 100644
--- a/myst_nb/core/execute/base.py
+++ b/myst_nb/core/execute/base.py
@@ -2,7 +2,6 @@
 from __future__ import annotations
 
 from pathlib import Path
-import re
 from typing import Any
 
 from nbformat import NotebookNode
@@ -39,9 +38,6 @@ class EvalNameError(Exception):
     """An exception for if an evaluation variable name is invalid."""
 
 
-EVAL_NAME_REGEX = re.compile(r"^[a-zA-Z_][a-zA-Z0-9_]*$")
-
-
 class NotebookClientBase:
     """A base client for interacting with Jupyter notebooks.
 
diff --git a/myst_nb/core/execute/inline.py b/myst_nb/core/execute/inline.py
index 06b53b07..13d20786 100644
--- a/myst_nb/core/execute/inline.py
+++ b/myst_nb/core/execute/inline.py
@@ -3,6 +3,7 @@
 
 import asyncio
 from datetime import datetime
+import re
 import shutil
 from tempfile import mkdtemp
 import time
@@ -22,7 +23,7 @@
 
 from myst_nb.ext.glue import extract_glue_data_cell
 
-from .base import EVAL_NAME_REGEX, EvalNameError, ExecutionError, NotebookClientBase
+from .base import EvalNameError, ExecutionError, NotebookClientBase
 
 
 class NotebookClientInline(NotebookClientBase):
@@ -148,7 +149,7 @@ def code_cell_outputs(
         return cell.get("execution_count", None), cell.get("outputs", [])
 
     def eval_variable(self, name: str) -> list[NotebookNode]:
-        if not EVAL_NAME_REGEX.match(name):
+        if not re.match(self.nb_config.eval_name_regex, name):
             raise EvalNameError(name)
         return self._client.eval_expression(name)
 
diff --git a/myst_nb/ext/eval/__init__.py b/myst_nb/ext/eval/__init__.py
index 3b565c74..52c04cd2 100644
--- a/myst_nb/ext/eval/__init__.py
+++ b/myst_nb/ext/eval/__init__.py
@@ -43,11 +43,13 @@ def retrieve_eval_data(document: nodes.document, key: str) -> list[VariableOutpu
     except NotImplementedError:
         raise RetrievalError("This document does not have a running kernel")
     except EvalNameError:
-        raise RetrievalError(f"The variable {key!r} is not a valid name")
+        raise RetrievalError(
+            f"The expression {key!r} is not valid according to the configured pattern"
+        )
     except Exception as exc:
         raise RetrievalError(f"variable evaluation error: {exc}")
     if not outputs:
-        raise RetrievalError(f"variable {key!r} does not return any outputs")
+        raise RetrievalError(f"expression {key!r} does not return any outputs")
 
     # the returned outputs could be one of the following:
     # https://nbformat.readthedocs.io/en/latest/format_description.html#code-cell-outputs