Index: llvm/test/tools/llvm-objcopy/ELF/rename-section-dynrelocsec.test
===================================================================
--- /dev/null
+++ llvm/test/tools/llvm-objcopy/ELF/rename-section-dynrelocsec.test
@@ -0,0 +1,24 @@
+# RUN: yaml2obj %s -o %t
+# RUN: llvm-objcopy --rename-section=.rela.plt=.rela.plt2 %t %t2
+# RUN: llvm-readobj --sections %t2 | FileCheck %s
+
+## Check that a dynamic relocation section can be renamed using an explicit
+## --rename-section. That resembles the behavior of GNU objcopy.
+
+--- !ELF
+FileHeader:
+  Class:   ELFCLASS64
+  Data:    ELFDATA2LSB
+  Type:    ET_EXEC
+  Machine: EM_X86_64
+Sections:
+  - Name:  .rela.plt
+    Type:  SHT_RELA
+    Flags: [ SHF_ALLOC ]
+    Link:  0
+  - Name:  .plt
+    Type:  SHT_PROGBITS
+    Flags: [ SHF_ALLOC, SHF_EXECINSTR ]
+
+# CHECK: Name: .rela.plt2
+# CHECK: Name: .plt
Index: llvm/test/tools/llvm-objcopy/ELF/rename-section-relocsec.test
===================================================================
--- /dev/null
+++ llvm/test/tools/llvm-objcopy/ELF/rename-section-relocsec.test
@@ -0,0 +1,31 @@
+# RUN: yaml2obj %s -o %t
+# RUN: llvm-objcopy --rename-section=.text=.text2 --rename-section=.data=.data2 %t %t2
+# RUN: llvm-readobj --sections %t2 | FileCheck %s
+
+## Check that when renaming a section then the corresponding relocation section
+## is renamed similarly.
+
+!ELF
+FileHeader:
+  Class:           ELFCLASS64
+  Data:            ELFDATA2LSB
+  Type:            ET_REL
+  Machine:         EM_X86_64
+Sections:
+  - Name:            .text
+    Type:            SHT_PROGBITS
+    Flags:           [ SHF_ALLOC ]
+  - Name:            .rel.text
+    Type:            SHT_REL
+    Info:            .text
+  - Name:            .rela.data
+    Type:            SHT_RELA
+    Info:            .data
+  - Name:            .data
+    Type:            SHT_PROGBITS
+    Flags:           [ SHF_ALLOC ]
+
+# CHECK: Name: .text2
+# CHECK: Name: .rel.text2
+# CHECK: Name: .rela.data2
+# CHECK: Name: .data2
Index: llvm/tools/llvm-objcopy/ELF/ELFObjcopy.cpp
===================================================================
--- llvm/tools/llvm-objcopy/ELF/ELFObjcopy.cpp
+++ llvm/tools/llvm-objcopy/ELF/ELFObjcopy.cpp
@@ -588,15 +588,33 @@
     return E;
 
   if (!Config.SectionsToRename.empty()) {
+    std::vector<RelocationSectionBase *> RelocSections;
+    DenseSet<SectionBase *> RenamedSections;
     for (SectionBase &Sec : Obj.sections()) {
+      // Postpone processing relocation sections until after their target
+      // sections are renamed.
+      // Dynamic relocation sections (i.e. SHT_REL[A] with SHF_ALLOC) should be
+      // renamed as normal sections to match the behavior of GNU objcopy.
+      auto *RelocSec = dyn_cast<RelocationSectionBase>(&Sec);
+      if (RelocSec && !(Sec.Flags & SHF_ALLOC)) {
+        RelocSections.push_back(RelocSec);
+        continue;
+      }
       const auto Iter = Config.SectionsToRename.find(Sec.Name);
       if (Iter != Config.SectionsToRename.end()) {
         const SectionRename &SR = Iter->second;
         Sec.Name = std::string(SR.NewName);
         if (SR.NewFlags.hasValue())
           setSectionFlagsAndType(Sec, SR.NewFlags.getValue());
+        RenamedSections.insert(&Sec);
       }
     }
+    // Rename relocation sections similarly to their targets.
+    for (RelocationSectionBase *RelocSec : RelocSections) {
+      auto Iter = RenamedSections.find(RelocSec->getSection());
+      if (Iter != RenamedSections.end())
+        RelocSec->Name = (RelocSec->getPrefix() + (*Iter)->Name).str();
+    }
   }
 
   // Add a prefix to allocated sections and their relocation sections. This