diff --git a/datafusion/expr/src/aggregate_function.rs b/datafusion/expr/src/aggregate_function.rs
index eaf4ff5ad806..ea0b01825170 100644
--- a/datafusion/expr/src/aggregate_function.rs
+++ b/datafusion/expr/src/aggregate_function.rs
@@ -116,13 +116,13 @@ impl AggregateFunction {
             ArrayAgg => "ARRAY_AGG",
             FirstValue => "FIRST_VALUE",
             LastValue => "LAST_VALUE",
-            Variance => "VARIANCE",
-            VariancePop => "VARIANCE_POP",
+            Variance => "VAR",
+            VariancePop => "VAR_POP",
             Stddev => "STDDEV",
             StddevPop => "STDDEV_POP",
-            Covariance => "COVARIANCE",
-            CovariancePop => "COVARIANCE_POP",
-            Correlation => "CORRELATION",
+            Covariance => "COVAR",
+            CovariancePop => "COVAR_POP",
+            Correlation => "CORR",
             RegrSlope => "REGR_SLOPE",
             RegrIntercept => "REGR_INTERCEPT",
             RegrCount => "REGR_COUNT",
@@ -411,3 +411,24 @@ impl AggregateFunction {
         }
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use strum::IntoEnumIterator;
+
+    #[test]
+    // Test for AggregateFuncion's Display and from_str() implementations.
+    // For each variant in AggregateFuncion, it converts the variant to a string
+    // and then back to a variant. The test asserts that the original variant and
+    // the reconstructed variant are the same. This assertion is also necessary for
+    // function suggestion. See https://github.com/apache/arrow-datafusion/issues/8082
+    fn test_display_and_from_str() {
+        for func_original in AggregateFunction::iter() {
+            let func_name = func_original.to_string();
+            let func_from_str =
+                AggregateFunction::from_str(func_name.to_lowercase().as_str()).unwrap();
+            assert_eq!(func_from_str, func_original);
+        }
+    }
+}
diff --git a/datafusion/expr/src/built_in_function.rs b/datafusion/expr/src/built_in_function.rs
index 16187572c521..1ebd9cc0187a 100644
--- a/datafusion/expr/src/built_in_function.rs
+++ b/datafusion/expr/src/built_in_function.rs
@@ -1621,7 +1621,8 @@ mod tests {
     // Test for BuiltinScalarFunction's Display and from_str() implementations.
     // For each variant in BuiltinScalarFunction, it converts the variant to a string
     // and then back to a variant. The test asserts that the original variant and
-    // the reconstructed variant are the same.
+    // the reconstructed variant are the same. This assertion is also necessary for
+    // function suggestion. See https://github.com/apache/arrow-datafusion/issues/8082
     fn test_display_and_from_str() {
         for (_, func_original) in name_to_function().iter() {
             let func_name = func_original.to_string();
diff --git a/datafusion/expr/src/window_function.rs b/datafusion/expr/src/window_function.rs
index e5b00c8f298b..463cceafeb6e 100644
--- a/datafusion/expr/src/window_function.rs
+++ b/datafusion/expr/src/window_function.rs
@@ -281,6 +281,7 @@ impl BuiltInWindowFunction {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use strum::IntoEnumIterator;
 
     #[test]
     fn test_count_return_type() -> Result<()> {
@@ -447,4 +448,18 @@ mod tests {
         );
         assert_eq!(find_df_window_func("not_exist"), None)
     }
+
+    #[test]
+    // Test for BuiltInWindowFunction's Display and from_str() implementations.
+    // For each variant in BuiltInWindowFunction, it converts the variant to a string
+    // and then back to a variant. The test asserts that the original variant and
+    // the reconstructed variant are the same. This assertion is also necessary for
+    // function suggestion. See https://github.com/apache/arrow-datafusion/issues/8082
+    fn test_display_and_from_str() {
+        for func_original in BuiltInWindowFunction::iter() {
+            let func_name = func_original.to_string();
+            let func_from_str = BuiltInWindowFunction::from_str(&func_name).unwrap();
+            assert_eq!(func_from_str, func_original);
+        }
+    }
 }
diff --git a/datafusion/sqllogictest/test_files/functions.slt b/datafusion/sqllogictest/test_files/functions.slt
index e3e39ef6cc4c..2054752cc59c 100644
--- a/datafusion/sqllogictest/test_files/functions.slt
+++ b/datafusion/sqllogictest/test_files/functions.slt
@@ -494,6 +494,10 @@ SELECT counter(*) from test;
 statement error Did you mean 'STDDEV'?
 SELECT STDEV(v1) from test;
 
+# Aggregate function
+statement error Did you mean 'COVAR'?
+SELECT COVARIA(1,1);
+
 # Window function
 statement error Did you mean 'SUM'?
 SELECT v1, v2, SUMM(v2) OVER(ORDER BY v1) from test;