diff --git a/CHANGELOG.md b/CHANGELOG.md
index fee7c50ed..6ad3d6ad2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -3,6 +3,7 @@
 ### Fixes
 
 - Persist table comments for incremental models, snapshots and dbt clone (thanks @henlue!) ([750](https://github.com/databricks/dbt-databricks/pull/750))
+- Add relation identifier (i.e. table name) in auto generated constraint names, also adding the statement of table list for foreign keys (thanks @elca-anh!) ([774](https://github.com/databricks/dbt-databricks/pull/774))
 - Update tblproperties on incremental runs. Note: only adds/edits. Deletes are too risky/complex for now ([765](https://github.com/databricks/dbt-databricks/pull/765))
 - Update default scope/redirect Url for OAuth U2M, so with default OAuth app user can run python models ([776](https://github.com/databricks/dbt-databricks/pull/776))
 
diff --git a/dbt/include/databricks/macros/relations/constraints.sql b/dbt/include/databricks/macros/relations/constraints.sql
index 91fcfa8d1..2132d4684 100644
--- a/dbt/include/databricks/macros/relations/constraints.sql
+++ b/dbt/include/databricks/macros/relations/constraints.sql
@@ -105,9 +105,13 @@
     {% endif %}
 
     {% set name = constraint.get("name") %}
-    {% if not name and local_md5 %}
-      {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead.") }}
-      {%- set name = local_md5 (column.get("name", "") ~ ";" ~ expression ~ ";") -%}
+    {% if not name %}
+      {% if local_md5 %}
+        {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead for relation " ~ relation.identifier) }}
+        {%- set name = local_md5 (relation.identifier ~ ";" ~ column.get("name", "") ~ ";" ~ expression ~ ";") -%}
+      {% else %}
+        {{ exceptions.raise_compiler_error("Constraint of type " ~ type ~ " with no `name` provided, and no md5 utility.") }}
+      {% endif %}
     {% endif %}
     {% set stmt = "alter table " ~ relation ~ " add constraint " ~ name ~ " check (" ~ expression ~ ");" %}
     {% do statements.append(stmt) %}
@@ -148,9 +152,13 @@
     {% set joined_names = quoted_names|join(", ") %}
 
     {% set name = constraint.get("name") %}
-    {% if not name and local_md5 %}
-      {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead.") }}
-      {%- set name = local_md5("primary_key;" ~ column_names ~ ";") -%}
+    {% if not name %}
+      {% if local_md5 %}
+        {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead for relation " ~ relation.identifier) }}
+        {%- set name = local_md5("primary_key;" ~ relation.identifier ~ ";" ~ column_names ~ ";") -%}
+      {% else %}
+        {{ exceptions.raise_compiler_error("Constraint of type " ~ type ~ " with no `name` provided, and no md5 utility.") }}
+      {% endif %}
     {% endif %}
     {% set stmt = "alter table " ~ relation ~ " add constraint " ~ name ~ " primary key(" ~ joined_names ~ ");" %}
     {% do statements.append(stmt) %}
@@ -161,12 +169,18 @@
     {% endif %}
 
     {% set name = constraint.get("name") %}
-    {% if not name and local_md5 %}
-      {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead.") }}
-      {%- set name = local_md5("primary_key;" ~ column_names ~ ";") -%}
-    {% endif %}
-
+    
     {% if constraint.get('expression') %}
+
+      {% if not name %}
+        {% if local_md5 %}
+          {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead for relation " ~ relation.identifier) }}
+          {%- set name = local_md5("foreign_key;" ~ relation.identifier ~ ";" ~ constraint.get('expression') ~ ";") -%}
+        {% else %}
+          {{ exceptions.raise_compiler_error("Constraint of type " ~ type ~ " with no `name` provided, and no md5 utility.") }}
+        {% endif %}    
+      {% endif %}
+
       {% set stmt = "alter table " ~ relation ~ " add constraint " ~ name ~ " foreign key" ~ constraint.get('expression') %}
     {% else %}
       {% set column_names = constraint.get("columns", []) %}
@@ -193,6 +207,16 @@
       {% if not "." in parent %}
         {% set parent = relation.schema ~ "." ~ parent%}
       {% endif %}
+
+      {% if not name %}
+        {% if local_md5 %}
+          {{ exceptions.warn("Constraint of type " ~ type ~ " with no `name` provided. Generating hash instead for relation " ~ relation.identifier) }}
+          {%- set name = local_md5("foreign_key;" ~ relation.identifier ~ ";" ~ column_names ~ ";" ~ parent ~ ";") -%}
+        {% else %}
+          {{ exceptions.raise_compiler_error("Constraint of type " ~ type ~ " with no `name` provided, and no md5 utility.") }}
+        {% endif %}    
+      {% endif %}
+
       {% set stmt = "alter table " ~ relation ~ " add constraint " ~ name ~ " foreign key(" ~ joined_names ~ ") references " ~ parent %}
       {% set parent_columns = constraint.get("parent_columns") %}
       {% if parent_columns %}
diff --git a/tests/unit/macros/relations/test_constraint_macros.py b/tests/unit/macros/relations/test_constraint_macros.py
index b316adbf9..0bbc3bdba 100644
--- a/tests/unit/macros/relations/test_constraint_macros.py
+++ b/tests/unit/macros/relations/test_constraint_macros.py
@@ -12,6 +12,11 @@ def template_name(self) -> str:
     def macro_folders_to_load(self) -> list:
         return ["macros/relations", "macros"]
 
+    @pytest.fixture(scope="class", autouse=True)
+    def modify_context(self, default_context) -> None:
+        # Mock local_md5
+        default_context["local_md5"] = lambda s: f"hash({s})"
+
     def render_constraints(self, template, *args):
         return self.run_macro(template, "databricks_constraints_to_dbt", *args)
 
@@ -240,7 +245,7 @@ def test_macros_get_constraint_sql_check_named_constraint(self, template_bundle,
         )
         assert expected in r
 
-    def test_macros_get_constraint_sql_check_none_constraint(self, template_bundle, model):
+    def test_macros_get_constraint_sql_check_noname_constraint(self, template_bundle, model):
         constraint = {
             "type": "check",
             "expression": "id != name",
@@ -248,7 +253,8 @@ def test_macros_get_constraint_sql_check_none_constraint(self, template_bundle,
         r = self.render_constraint_sql(template_bundle, constraint, model)
 
         expected = (
-            "['alter table `some_database`.`some_schema`.`some_table` add constraint None "
+            "['alter table `some_database`.`some_schema`.`some_table` "
+            "add constraint hash(some_table;;id != name;) "
             "check (id != name);']"
         )  # noqa: E501
         assert expected in r
@@ -307,6 +313,19 @@ def test_macros_get_constraint_sql_primary_key_with_name(self, template_bundle,
         )
         assert expected in r
 
+    def test_macros_get_constraint_sql_primary_key_noname(self, template_bundle, model):
+        constraint = {"type": "primary_key"}
+        column = {"name": "id"}
+
+        r = self.render_constraint_sql(template_bundle, constraint, model, column)
+
+        expected = (
+            '["alter table `some_database`.`some_schema`.`some_table` add constraint '
+            "hash(primary_key;some_table;['id'];) "
+            'primary key(id);"]'
+        )
+        assert expected in r
+
     def test_macros_get_constraint_sql_foreign_key(self, template_bundle, model):
         constraint = {
             "type": "foreign_key",
@@ -323,6 +342,21 @@ def test_macros_get_constraint_sql_foreign_key(self, template_bundle, model):
         )
         assert expected in r
 
+    def test_macros_get_constraint_sql_foreign_key_noname(self, template_bundle, model):
+        constraint = {
+            "type": "foreign_key",
+            "columns": ["name"],
+            "parent": "parent_table",
+        }
+        r = self.render_constraint_sql(template_bundle, constraint, model)
+
+        expected = (
+            '["alter table `some_database`.`some_schema`.`some_table` add '
+            "constraint hash(foreign_key;some_table;['name'];some_schema.parent_table;) "
+            'foreign key(name) references some_schema.parent_table;"]'
+        )
+        assert expected in r
+
     def test_macros_get_constraint_sql_foreign_key_parent_column(self, template_bundle, model):
         constraint = {
             "type": "foreign_key",