diff --git a/Makefile b/Makefile
index cf87511e2..9ecf3470a 100644
--- a/Makefile
+++ b/Makefile
@@ -215,7 +215,7 @@ blah:
 	@echo ${PACKAGES}
 
 ocaml-versions/%.bench: depend filter/% override_packages/% log_sandmark_hash ocaml-versions/%.json .FORCE
-	$(eval SANDMARK_CUSTOM_NAME ?= $*)
+	$(eval VARIANT_NAME ?= $*)
 	$(eval CONFIG_SWITCH_NAME = $*)
 	$(eval CONFIG_OPTIONS      = $(shell jq -r '.configure // empty' ocaml-versions/$*.json))
 	$(eval CONFIG_RUN_PARAMS   = $(shell jq -r '.runparams // empty' ocaml-versions/$*.json))
@@ -245,8 +245,8 @@ ocaml-versions/%.bench: depend filter/% override_packages/% log_sandmark_hash oc
 			fi; \
 			done; \
 			header_entry=`jo -p $${s} | jq -c`; \
-			echo "$${header_entry}" > _results/$(SANDMARK_CUSTOM_NAME)_$$i.$(WRAPPER).summary.bench; \
-			find _build/$(CONFIG_SWITCH_NAME)_$$i -name '*.$(WRAPPER).bench' | xargs cat >> _results/$(SANDMARK_CUSTOM_NAME)_$$i.$(WRAPPER).summary.bench;		\
+			echo "$${header_entry}" > _results/$(VARIANT_NAME)_$$i.$(WRAPPER).summary.bench; \
+			find _build/$(CONFIG_SWITCH_NAME)_$$i -name '*.$(WRAPPER).bench' | xargs cat >> _results/$(VARIANT_NAME)_$$i.$(WRAPPER).summary.bench;		\
 		done;															\
 		exit $$ex;														\
 	   else																\
diff --git a/README.md b/README.md
index 6ed87cada..fefaffb00 100644
--- a/README.md
+++ b/README.md
@@ -210,7 +210,7 @@ benchmarks in byte mode:
 
 ```bash
 $ opam install dune.2.9.0
-$ USE_SYS_DUNE_HACK=1 SANDMARK_CUSTOM_NAME=5.0.0 BUILD_BENCH_TARGET=bytebench \
+$ USE_SYS_DUNE_HACK=1 VARIANT_NAME=5.0.0 BUILD_BENCH_TARGET=bytebench \
     RUN_CONFIG_JSON=run_config_byte.json make ocaml-versions/5.0.0+stable.bench
 ```
 
@@ -369,11 +369,11 @@ work on OS X is to install GNU sed with homebrew and then update the
 | PRE_BENCH_EXEC | Any specific commands that needed to be executed before the benchmark. For eg. `PRE_BENCH_EXEC='taskset --cpu-list 3 setarch uname -m --addr-no-randomize'` | null string | executing benchmark | RUN_BENCH_TARGET | The executable to be used to run the benchmarks | `run_orun` | executing benchmark |
 | RUN_BENCH_TARGET | The executable to be used to run the benchmarks | `run_orun` | executing benchmark |
 | RUN_CONFIG_JSON | Input file selection that contains the list of benchmarks | `run_config.json` | executing benchmark |
-| SANDMARK_CUSTOM_NAME | Custom name to use for the bench output file | variant from the `ocaml-version/<variant>.json` file name | executing benchmark |
 | SANDMARK_DUNE_VERSION | Default dune version to be used | 2.9.0 | building compiler and its dependencies |
 | SANDMARK_OVERRIDE_PACKAGES | A list of dependency packages with versions that can be overrided (optional) | "" | building compiler and its dependencies |
 | SANDMARK_REMOVE_PACKAGES | A list of dependency packages to be dynamically removed (optional) | "" | building compiler and its dependencies |
 | SANDMARK_URL | OCaml compiler source code URL used to build the benchmarks | "" | building compiler and its dependencies |
 | SYS_DUNE_BASE_DIR | Function that returns the path of the system installed dune for use with benchmarking | dune package present in the local opam switch | building compiler and its dependencies |
 | USE_SYS_DUNE_HACK | If the value is 1 then use system installed dune | 0 | building compiler and its dependencies |
+| VARIANT_NAME | Custom name to use for the bench output file | variant from the `ocaml-version/<variant>.json` file name | executing benchmark |
 | WRAPPER | Function to get the wrapper out of `run_<wrapper-name>` | run_orun | executing benchmark |
diff --git a/run_all_custom.sh b/run_all_custom.sh
index 4b71f9fa1..e12746378 100755
--- a/run_all_custom.sh
+++ b/run_all_custom.sh
@@ -126,7 +126,7 @@ while [ $i -lt ${COUNT} ]; do
                                  ENVIRONMENT="`echo ${CONFIG_ENVIRONMENT}`" \
                                  OCAML_CONFIG_OPTION="`echo ${CONFIG_OPTIONS}`" \
                                  OCAML_RUN_PARAM="`echo ${CONFIG_RUN_PARAMS}`" \
-                                 SANDMARK_CUSTOM_NAME="`echo ${CONFIG_NAME}`" \
+                                 VARIANT_NAME="`echo ${CONFIG_NAME}`" \
                                  SANDMARK_OVERRIDE_PACKAGES="`echo ${CONFIG_OVERRIDE_PACKAGES}`" \
                                  SANDMARK_REMOVE_PACKAGES="`echo ${CONFIG_REMOVE_PACKAGES}`" \
                                  make ocaml-versions/5.1.0+stable.bench > "${RESULTS_DIR}/${CONFIG_NAME}.${TIMESTAMP}.${COMMIT}.log" 2>&1
@@ -147,7 +147,7 @@ while [ $i -lt ${COUNT} ]; do
                                  ENVIRONMENT="`echo ${CONFIG_ENVIRONMENT}`" \
                                  OCAML_CONFIG_OPTION="`echo ${CONFIG_OPTIONS}`" \
                                  OCAML_RUN_PARAM="`echo ${CONFIG_RUN_PARAMS}`" \
-                                 SANDMARK_CUSTOM_NAME="`echo ${CONFIG_NAME}`" \
+                                 VARIANT_NAME="`echo ${CONFIG_NAME}`" \
                                  SANDMARK_OVERRIDE_PACKAGES="`echo ${CONFIG_OVERRIDE_PACKAGES}`" \
                                  SANDMARK_REMOVE_PACKAGES="`echo ${CONFIG_REMOVE_PACKAGES}`" \
                                  RUN_BENCH_TARGET=run_orunchrt \