diff --git a/dokimi/changelog.d/20261024_121000_napetrov_run-container-name.md b/dokimi/changelog.d/20261024_121000_napetrov_run-container-name.md
new file mode 100644
index 00000000..65ac3321
--- /dev/null
+++ b/dokimi/changelog.d/20261024_121000_napetrov_run-container-name.md
@@ -0,0 +1,5 @@
+### Fixed
+
+- **Two `docker-*` cells of one task in one process no longer share a
+  container name** — the name `dokimi-run-<task>-<pid>` gets a random suffix,
+  so one cell's cleanup cannot remove the other's container.
diff --git a/dokimi/dokimi/harnesses/docker_solver.py b/dokimi/dokimi/harnesses/docker_solver.py
index 52d5ae20..ce26b6b5 100644
--- a/dokimi/dokimi/harnesses/docker_solver.py
+++ b/dokimi/dokimi/harnesses/docker_solver.py
@@ -205,7 +205,7 @@ def run(
         log = log_path.open("w", encoding="utf-8")
         usage: Optional[UsageRecord] = None
         image = f"dokimi/{task.name}:latest"
-        container = f"dokimi-run-{task.name}-{os.getpid()}"
+        container = f"dokimi-run-{task.name}-{os.getpid()}-{os.urandom(3).hex()}"  # two cells in one process
         solve_timeout = timeout_sec or task.timeout_sec or _DEFAULT_SOLVE_TIMEOUT
         start = time.time()
         returncode = 0
diff --git a/dokimi/tests/test_run_container_name.py b/dokimi/tests/test_run_container_name.py
new file mode 100644
index 00000000..d04129f8
--- /dev/null
+++ b/dokimi/tests/test_run_container_name.py
@@ -0,0 +1,30 @@
+# Copyright (C) 2026 Intel Corporation
+# SPDX-License-Identifier: Apache-2.0
+
+"""The docker-* task container's name is unique per cell, not per process."""
+
+from __future__ import annotations
+
+from dokimi.harnesses import load_task
+from dokimi.harnesses.registry import create_harness
+from docker_cli_fake import DockerCLI
+
+
+def test_two_runs_of_one_task_in_one_process_get_their_own_container(tmp_path):
+    # A suite runs every harness cell in one process: a pid-only name made the
+    # second cell's `docker rm -f` remove the first cell's container.
+    task_dir = tmp_path / "t"
+    for d in ("tests", "environment", "solution"):
+        (task_dir / d).mkdir(parents=True)
+    (task_dir / "instruction.md").write_text("x", encoding="utf-8")
+    (task_dir / "task.toml").write_text("[metadata]\ntags = []\n", encoding="utf-8")
+    task = load_task(task_dir)
+    names = set()
+    for arm in ("a", "b"):
+        cli = DockerCLI()
+        create_harness("docker-oracle", runner=cli).run(task, output_dir=tmp_path / arm)
+        (name,) = {a[a.index("--name") + 1] for a in cli.args if a[0] == "run"}
+        # every `docker rm -f` of this arm must name this arm's container
+        assert {a[-1] for a in cli.args if a[0] == "rm"} == {name}
+        names.add(name)
+    assert len(names) == 2 and all(n.startswith(f"dokimi-run-{task.name}-") for n in names)