diff --git a/llvm/lib/CodeGen/AsmPrinter/AccelTable.cpp b/llvm/lib/CodeGen/AsmPrinter/AccelTable.cpp
--- a/llvm/lib/CodeGen/AsmPrinter/AccelTable.cpp
+++ b/llvm/lib/CodeGen/AsmPrinter/AccelTable.cpp
@@ -270,7 +270,7 @@
         continue;
       PrevHash = HashValue;
       Asm->OutStreamer->AddComment("Offset in Bucket " + Twine(i));
-      Asm->emitLabelDifference(Hash->Sym, Base, sizeof(uint32_t));
+      Asm->emitLabelDifference(Hash->Sym, Base, Asm->getDwarfOffsetByteSize());
     }
   }
 }
@@ -366,9 +366,8 @@
   assert(CompUnitCount > 0 && "Index must have at least one CU.");
 
   AsmPrinter *Asm = Ctx.Asm;
-  Asm->OutStreamer->AddComment("Header: unit length");
-  Asm->emitLabelDifference(Ctx.ContributionEnd, Ctx.ContributionStart,
-                           sizeof(uint32_t));
+  Asm->emitDwarfUnitLength(Ctx.ContributionEnd, Ctx.ContributionStart,
+                           "Header: unit length");
   Asm->OutStreamer->emitLabel(Ctx.ContributionStart);
   Asm->OutStreamer->AddComment("Header: version");
   Asm->emitInt16(Version);
diff --git a/llvm/test/DebugInfo/X86/debug-names-dwarf64.ll b/llvm/test/DebugInfo/X86/debug-names-dwarf64.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/DebugInfo/X86/debug-names-dwarf64.ll
@@ -0,0 +1,87 @@
+; This checks that .debug_names can be generated in the DWARF64 format.
+
+; RUN: llc -mtriple=x86_64 -dwarf64 -accel-tables=Dwarf -dwarf-version=5 -filetype=obj %s -o %t
+; RUN: llvm-dwarfdump -debug-info -debug-names %t | FileCheck %s
+; RUN: llvm-dwarfdump -debug-names -verify %t | FileCheck --check-prefix=VERIFY %s
+
+; CHECK:     .debug_info contents:
+; CHECK-NEXT: 0x00000000:     Compile Unit: {{.+}}, format = DWARF64,
+; CHECK:      [[VARDIE:.+]]:  DW_TAG_variable
+; CHECK-NEXT:                   DW_AT_name ("foo")
+; CHECK:      [[TYPEDIE:.+]]: DW_TAG_base_type
+; CHECK-NEXT:                   DW_AT_name ("int")
+
+; CHECK:      .debug_names contents:
+; CHECK-NEXT: Name Index @ 0x0 {
+; CHECK-NEXT:   Header {
+; CHECK:          Format: DWARF64
+; CHECK-NEXT:     Version: 5
+; CHECK-NEXT:     CU count: 1
+; CHECK-NEXT:     Local TU count: 0
+; CHECK-NEXT:     Foreign TU count: 0
+; CHECK-NEXT:     Bucket count: 2
+; CHECK-NEXT:     Name count: 2
+; CHECK:        }
+; CHECK-NEXT:   Compilation Unit offsets [
+; CHECK-NEXT:     CU[0]: 0x00000000
+; CHECK-NEXT:   ]
+; CHECK-NEXT:   Abbreviations [
+; CHECK-NEXT:     Abbreviation 0x34 {
+; CHECK-NEXT:       Tag: DW_TAG_variable
+; CHECK-NEXT:       DW_IDX_die_offset: DW_FORM_ref4
+; CHECK-NEXT:     }
+; CHECK-NEXT:     Abbreviation 0x24 {
+; CHECK-NEXT:       Tag: DW_TAG_base_type
+; CHECK-NEXT:       DW_IDX_die_offset: DW_FORM_ref4
+; CHECK-NEXT:     }
+; CHECK-NEXT:   ]
+; CHECK-NEXT:   Bucket 0 [
+; CHECK-NEXT:     Name 1 {
+; CHECK-NEXT:       Hash: 0xB888030
+; CHECK-NEXT:       String: {{.+}} "int"
+; CHECK-NEXT:       Entry @ {{.+}} {
+; CHECK-NEXT:         Abbrev: 0x24
+; CHECK-NEXT:         Tag: DW_TAG_base_type
+; CHECK-NEXT:         DW_IDX_die_offset: [[TYPEDIE]]
+; CHECK-NEXT:       }
+; CHECK-NEXT:     }
+; CHECK-NEXT:   ]
+; CHECK-NEXT:   Bucket 1 [
+; CHECK-NEXT:     Name 2 {
+; CHECK-NEXT:       Hash: 0xB887389
+; CHECK-NEXT:       String: {{.+}} "foo"
+; CHECK-NEXT:       Entry @ {{.+}} {
+; CHECK-NEXT:         Abbrev: 0x34
+; CHECK-NEXT:         Tag: DW_TAG_variable
+; CHECK-NEXT:         DW_IDX_die_offset: [[VARDIE]]
+; CHECK-NEXT:       }
+; CHECK-NEXT:     }
+; CHECK-NEXT:   ]
+; CHECK-NEXT: }
+
+; VERIFY: No errors.
+
+; IR generated and reduced from:
+; $ cat foo.c
+; int foo;
+; $ clang -g -gpubnames -S -emit-llvm foo.c -o foo.ll
+
+target triple = "x86_64-unknown-linux-gnu"
+
+@foo = dso_local global i32 0, align 4, !dbg !0
+
+!llvm.dbg.cu = !{!2}
+!llvm.module.flags = !{!7, !8, !9}
+!llvm.ident = !{!10}
+
+!0 = !DIGlobalVariableExpression(var: !1, expr: !DIExpression())
+!1 = distinct !DIGlobalVariable(name: "foo", scope: !2, file: !3, line: 1, type: !6, isLocal: false, isDefinition: true)
+!2 = distinct !DICompileUnit(language: DW_LANG_C99, file: !3, producer: "clang version 12.0.0", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug, enums: !4, globals: !5, splitDebugInlining: false)
+!3 = !DIFile(filename: "foo.c", directory: "/tmp")
+!4 = !{}
+!5 = !{!0}
+!6 = !DIBasicType(name: "int", size: 32, encoding: DW_ATE_signed)
+!7 = !{i32 7, !"Dwarf Version", i32 4}
+!8 = !{i32 2, !"Debug Info Version", i32 3}
+!9 = !{i32 1, !"wchar_size", i32 4}
+!10 = !{!"clang version 12.0.0"}