diff --git a/ci/test/00_setup_env.sh b/ci/test/00_setup_env.sh
index 4fdfa779ae..21fa373fcb 100755
--- a/ci/test/00_setup_env.sh
+++ b/ci/test/00_setup_env.sh
@@ -39,6 +39,7 @@ export USE_BUSY_BOX=${USE_BUSY_BOX:-false}
 export RUN_UNIT_TESTS=${RUN_UNIT_TESTS:-true}
 export RUN_INTEGRATION_TESTS=${RUN_INTEGRATION_TESTS:-true}
 export RUN_FUZZ_TESTS=${RUN_FUZZ_TESTS:-false}
+export CONTAINER_NAME=${CONTAINER_NAME:-ci_unnamed}
 export DOCKER_NAME_TAG=${DOCKER_NAME_TAG:-ubuntu:focal}
 # Randomize test order.
 # See https://www.boost.org/doc/libs/1_71_0/libs/test/doc/html/boost_test/utf_reference/rt_param_reference/random.html
diff --git a/ci/test/00_setup_env_arm.sh b/ci/test/00_setup_env_arm.sh
index fefc9c11f2..743fbb9558 100755
--- a/ci/test/00_setup_env_arm.sh
+++ b/ci/test/00_setup_env_arm.sh
@@ -16,6 +16,7 @@ if [ -n "$QEMU_USER_CMD" ]; then
   # Likely cross-compiling, so install the needed gcc and qemu-user
   export PACKAGES="$PACKAGES qemu-user"
 fi
+export CONTAINER_NAME=ci_arm_linux
 # Use debian to avoid 404 apt errors when cross compiling
 export DOCKER_NAME_TAG="debian:focal"
 export CHECK_DOC=1
diff --git a/ci/test/00_setup_env_i686_centos.sh b/ci/test/00_setup_env_i686_centos.sh
index 945628be8a..210e15968b 100644
--- a/ci/test/00_setup_env_i686_centos.sh
+++ b/ci/test/00_setup_env_i686_centos.sh
@@ -7,6 +7,7 @@
 export LC_ALL=C.UTF-8
 
 export HOST=i686-pc-linux-gnu
+export CONTAINER_NAME=ci_i686_centos_7
 export DOCKER_NAME_TAG=centos:7
 export DOCKER_PACKAGES="gcc-c++ glibc-devel.x86_64 libstdc++-devel.x86_64 glibc-devel.i686 libstdc++-devel.i686 ccache libtool make git python3 python36-zmq which patch lbzip2 dash"
 export GOAL="install"
diff --git a/ci/test/00_setup_env_mac.sh b/ci/test/00_setup_env_mac.sh
index 8f11a7d3a0..b31fd9f7e7 100755
--- a/ci/test/00_setup_env_mac.sh
+++ b/ci/test/00_setup_env_mac.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_macos_cross
 export HOST=x86_64-apple-darwin19
 export PACKAGES="cmake imagemagick libcap-dev librsvg2-bin libz-dev libbz2-dev libtiff-tools python3-dev python3-setuptools"
 export XCODE_VERSION=12.1
diff --git a/ci/test/00_setup_env_mac_host.sh b/ci/test/00_setup_env_mac_host.sh
index 7779a34e7f..6e23046b79 100755
--- a/ci/test/00_setup_env_mac_host.sh
+++ b/ci/test/00_setup_env_mac_host.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_macos
 export HOST=x86_64-apple-darwin19
 export BREW_PACKAGES="automake berkeley-db4 libtool boost miniupnpc pkg-config qt qrencode python3 ccache zeromq"
 export PIP_PACKAGES="zmq"
diff --git a/ci/test/00_setup_env_native_cxx20.sh b/ci/test/00_setup_env_native_cxx20.sh
index c17fd1e42e..6de18f16ee 100755
--- a/ci/test/00_setup_env_native_cxx20.sh
+++ b/ci/test/00_setup_env_native_cxx20.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_native_cxx20
 export PACKAGES="python3-zmq qtbase5-dev qttools5-dev-tools libdbus-1-dev libharfbuzz-dev"
 export DEP_OPTS="NO_UPNP=1 DEBUG=1"
 export CPPFLAGS="-DDEBUG_LOCKORDER -DENABLE_DASH_DEBUG -DARENA_DEBUG"
diff --git a/ci/test/00_setup_env_native_fuzz.sh b/ci/test/00_setup_env_native_fuzz.sh
index 000e0024ae..d552a9b912 100755
--- a/ci/test/00_setup_env_native_fuzz.sh
+++ b/ci/test/00_setup_env_native_fuzz.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_native_fuzz
 export PACKAGES="clang llvm python3 libevent-dev bsdmainutils libboost-filesystem-dev libboost-test-dev libboost-thread-dev"
 export DEP_OPTS="NO_UPNP=1 DEBUG=1"
 export CPPFLAGS="-DDEBUG_LOCKORDER -DENABLE_DASH_DEBUG -DARENA_DEBUG"
diff --git a/ci/test/00_setup_env_native_nowallet.sh b/ci/test/00_setup_env_native_nowallet.sh
index 8ef3bc1fc1..832884f0de 100755
--- a/ci/test/00_setup_env_native_nowallet.sh
+++ b/ci/test/00_setup_env_native_nowallet.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_native_nowallet
 export PACKAGES="python3-zmq"
 export DEP_OPTS="NO_WALLET=1"
 export GOAL="install"
diff --git a/ci/test/00_setup_env_native_qt5.sh b/ci/test/00_setup_env_native_qt5.sh
index e94202a21c..943fc494e2 100755
--- a/ci/test/00_setup_env_native_qt5.sh
+++ b/ci/test/00_setup_env_native_qt5.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_native_qt5
 export PACKAGES="python3-zmq qtbase5-dev qttools5-dev-tools libdbus-1-dev libharfbuzz-dev"
 export DEP_OPTS="NO_UPNP=1 DEBUG=1"
 # TODO: we have few rpcs that aren't covered by any test, re-enable the line below once it's fixed
diff --git a/ci/test/00_setup_env_native_sqlite.sh b/ci/test/00_setup_env_native_sqlite.sh
index e97fd0ebb9..a455ada871 100644
--- a/ci/test/00_setup_env_native_sqlite.sh
+++ b/ci/test/00_setup_env_native_sqlite.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_native_sqlite
 export PACKAGES="python3-zmq qtbase5-dev qttools5-dev-tools libdbus-1-dev libharfbuzz-dev"
 export DEP_OPTS="NO_BDB=1 NO_UPNP=1 DEBUG=1"
 export GOAL="install"
diff --git a/ci/test/00_setup_env_native_tsan.sh b/ci/test/00_setup_env_native_tsan.sh
index 169acde9d5..a34a226096 100755
--- a/ci/test/00_setup_env_native_tsan.sh
+++ b/ci/test/00_setup_env_native_tsan.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_native_tsan
 export PACKAGES="clang-8 llvm-8 python3-zmq qtbase5-dev qttools5-dev-tools libevent-dev bsdmainutils libboost-filesystem-dev libboost-test-dev libboost-thread-dev libdb5.3++-dev libminiupnpc-dev libzmq3-dev libqrencode-dev"
 export DEP_OPTS="NO_UPNP=1 DEBUG=1"
 export TEST_RUNNER_EXTRA="--extended --exclude feature_pruning,feature_dbcrash,wallet_multiwallet.py" # Temporarily suppress ASan heap-use-after-free (see issue #14163)
diff --git a/ci/test/00_setup_env_s390x.sh b/ci/test/00_setup_env_s390x.sh
index 2bf90f24a3..39c080a735 100644
--- a/ci/test/00_setup_env_s390x.sh
+++ b/ci/test/00_setup_env_s390x.sh
@@ -17,6 +17,7 @@ if [ -n "$QEMU_USER_CMD" ]; then
   export PACKAGES="$PACKAGES g++-s390x-linux-gnu qemu-user libc6:s390x libstdc++6:s390x libfontconfig1:s390x libxcb1:s390x"
 fi
 # Use debian to avoid 404 apt errors
+export CONTAINER_NAME=ci_s390x
 export DOCKER_NAME_TAG="debian:focal"
 export RUN_UNIT_TESTS=true
 export RUN_FUNCTIONAL_TESTS=true
diff --git a/ci/test/00_setup_env_win64.sh b/ci/test/00_setup_env_win64.sh
index b3365de25f..b7cc19acff 100755
--- a/ci/test/00_setup_env_win64.sh
+++ b/ci/test/00_setup_env_win64.sh
@@ -6,6 +6,7 @@
 
 export LC_ALL=C.UTF-8
 
+export CONTAINER_NAME=ci_win64
 export HOST=x86_64-w64-mingw32
 export PACKAGES="python3 nsis g++-mingw-w64-x86-64 wine-binfmt wine64"
 export DPKG_ADD_ARCH="i386"
diff --git a/ci/test/04_install.sh b/ci/test/04_install.sh
index 6f6ea2e81f..c5983c7d61 100755
--- a/ci/test/04_install.sh
+++ b/ci/test/04_install.sh
@@ -66,6 +66,7 @@ if [ -z "$RUN_CI_ON_HOST" ]; then
                   --mount type=bind,src=$DEPENDS_DIR,dst=$DEPENDS_DIR \
                   -w $BASE_ROOT_DIR \
                   --env-file /tmp/env \
+                  --name $CONTAINER_NAME \
                   $DOCKER_NAME_TAG)
 
   DOCKER_EXEC () {