diff --git a/datafusion/expr/src/expr.rs b/datafusion/expr/src/expr.rs
index 5d750083894c2..212ec1a7791b1 100644
--- a/datafusion/expr/src/expr.rs
+++ b/datafusion/expr/src/expr.rs
@@ -1631,6 +1631,16 @@ fn create_name(e: &Expr) -> Result<String> {
                 }
                 Ok(format!("{}({}){}", fun.name(), names.join(","), info))
             }
+            AggregateFunctionDefinition::Name(name) => {
+                let mut name = create_function_name(name, *distinct, args)?;
+                if let Some(fe) = filter {
+                    name = format!("{name} FILTER (WHERE {fe})");
+                };
+                if let Some(order_by) = order_by {
+                    name = format!("{name} ORDER BY [{}]", expr_vec_fmt!(order_by));
+                };
+                Ok(name)
+            }
         },
         Expr::GroupingSet(grouping_set) => match grouping_set {
             GroupingSet::Rollup(exprs) => {
diff --git a/datafusion/optimizer/src/analyzer/count_wildcard_rule.rs b/datafusion/optimizer/src/analyzer/count_wildcard_rule.rs
index 16d8c72d462a3..b63f1d21116d3 100644
--- a/datafusion/optimizer/src/analyzer/count_wildcard_rule.rs
+++ b/datafusion/optimizer/src/analyzer/count_wildcard_rule.rs
@@ -19,7 +19,7 @@ use crate::analyzer::AnalyzerRule;
 use datafusion_common::config::ConfigOptions;
 use datafusion_common::tree_node::{Transformed, TreeNode, TreeNodeRewriter};
 use datafusion_common::Result;
-use datafusion_expr::expr::{AggregateFunction, InSubquery};
+use datafusion_expr::expr::{AggregateFunction, AggregateFunctionDefinition, InSubquery};
 use datafusion_expr::expr_rewriter::rewrite_preserving_name;
 use datafusion_expr::utils::COUNT_STAR_EXPANSION;
 use datafusion_expr::Expr::ScalarSubquery;
@@ -144,7 +144,11 @@ impl TreeNodeRewriter for CountWildcardRewriter {
                 _ => old_expr,
             },
             Expr::AggregateFunction(AggregateFunction {
-                func_def: _,
+                func_def:
+                    AggregateFunctionDefinition::BuiltIn {
+                        fun: aggregate_function::AggregateFunction::Count,
+                        name: _,
+                    },
                 args,
                 distinct,
                 filter,
diff --git a/datafusion/optimizer/src/single_distinct_to_groupby.rs b/datafusion/optimizer/src/single_distinct_to_groupby.rs
index f66ff0eae6f0e..f3e29296d7a36 100644
--- a/datafusion/optimizer/src/single_distinct_to_groupby.rs
+++ b/datafusion/optimizer/src/single_distinct_to_groupby.rs
@@ -71,7 +71,7 @@ fn is_single_distinct_agg(plan: &LogicalPlan) -> Result<bool> {
             let mut aggregate_count = 0;
             for expr in aggr_expr {
                 if let Expr::AggregateFunction(AggregateFunction {
-                    func_def,
+                    func_def: AggregateFunctionDefinition::BuiltIn { fun, name: _ },
                     distinct,
                     args,
                     filter,
@@ -86,19 +86,8 @@ fn is_single_distinct_agg(plan: &LogicalPlan) -> Result<bool> {
                         for e in args {
                             fields_set.insert(e.canonical_name());
                         }
-                    } else {
-                        match func_def {
-                            AggregateFunctionDefinition::BuiltIn { fun, name: _ } => {
-                                if !matches!(fun, Sum | Min | Max) {
-                                    return Ok(false);
-                                } else {
-                                    return Ok(true);
-                                }
-                            }
-                            _ => {
-                                return Ok(false);
-                            }
-                        }
+                    } else if !matches!(fun, Sum | Min | Max) {
+                        return Ok(false);
                     }
                 }
             }