diff --git a/gopls/internal/lsp/source/rename.go b/gopls/internal/lsp/source/rename.go
index 02bdaededaf..0f49cdcd56b 100644
--- a/gopls/internal/lsp/source/rename.go
+++ b/gopls/internal/lsp/source/rename.go
@@ -350,8 +350,13 @@ func renameOrdinary(ctx context.Context, snapshot Snapshot, f FileHandle, pp pro
 		// So we take a scenic route.
 		switch obj.(type) { // avoid "obj :=" since cases reassign the var
 		case *types.TypeName:
-			if named, ok := obj.Type().(*types.Named); ok {
-				obj = named.Obj()
+			switch t := obj.Type().(type) {
+			case *types.Named:
+				obj = t.Obj()
+			case *typeparams.TypeParam:
+				// As with capitalized function parameters below, type parameters are
+				// local.
+				goto skipObjectPath
 			}
 		case *types.Func:
 			obj = funcOrigin(obj.(*types.Func))
diff --git a/gopls/internal/regtest/marker/testdata/rename/generics.txt b/gopls/internal/regtest/marker/testdata/rename/generics.txt
new file mode 100644
index 00000000000..6f308b126d4
--- /dev/null
+++ b/gopls/internal/regtest/marker/testdata/rename/generics.txt
@@ -0,0 +1,117 @@
+This test exercises various renaming features on generic code.
+
+Fixed bugs:
+
+- golang/go#61614: renaming a method of a type in a package that uses type
+  parameter composite lits used to panic, because previous iterations of the
+  satisfy analysis did not account for this language feature.
+
+- golang/go#61635: renaming type parameters did not work when they were
+  capitalized and the package was imported by another package.
+
+-- flags --
+-min_go=go1.18
+
+-- go.mod --
+module example.com
+go 1.20
+
+-- a.go --
+package a
+
+type I int
+
+func (I) m() {} //@rename("m", M, mToM)
+
+func _[P ~[]int]() {
+	_ = P{}
+}
+
+-- @mToM/a.go --
+package a
+
+type I int
+
+func (I) M() {} //@rename("m", M, mToM)
+
+func _[P ~[]int]() {
+	_ = P{}
+}
+
+-- g.go --
+package a
+
+type S[P any] struct { //@rename("P", Q, PToQ)
+	P P
+	F func(P) P
+}
+
+func F[R any](r R) {
+	var _ R //@rename("R", S, RToS)
+}
+
+-- @PToQ/g.go --
+package a
+
+type S[Q any] struct { //@rename("P", Q, PToQ)
+	P Q
+	F func(Q) Q
+}
+
+func F[R any](r R) {
+	var _ R //@rename("R", S, RToS)
+}
+
+-- @RToS/g.go --
+package a
+
+type S[P any] struct { //@rename("P", Q, PToQ)
+	P P
+	F func(P) P
+}
+
+func F[S any](r S) {
+	var _ S //@rename("R", S, RToS)
+}
+
+-- issue61635/p.go --
+package issue61635
+
+type builder[S ~[]F, F ~string] struct { //@rename("S", T, SToT)
+	name string
+	elements S
+	elemData map[F][]ElemData[F]
+	// other fields...
+}
+
+type ElemData[F ~string] struct {
+  Name F
+  // other fields...
+}
+
+type BuilderImpl[S ~[]F, F ~string] struct{ builder[S, F] }
+
+-- importer/i.go --
+package importer
+
+import "example.com/issue61635" // importing is necessary to repro golang/go#61635
+
+var _ issue61635.ElemData[string]
+
+-- @SToT/issue61635/p.go --
+package issue61635
+
+type builder[T ~[]F, F ~string] struct { //@rename("S", T, SToT)
+	name string
+	elements T
+	elemData map[F][]ElemData[F]
+	// other fields...
+}
+
+type ElemData[F ~string] struct {
+  Name F
+  // other fields...
+}
+
+type BuilderImpl[S ~[]F, F ~string] struct{ builder[S, F] }
+
diff --git a/gopls/internal/regtest/marker/testdata/rename/issue61614.txt b/gopls/internal/regtest/marker/testdata/rename/issue61614.txt
deleted file mode 100644
index cfb37b19ac5..00000000000
--- a/gopls/internal/regtest/marker/testdata/rename/issue61614.txt
+++ /dev/null
@@ -1,35 +0,0 @@
-This test renames a method of a type in a package that uses type parameter
-composite lits. Previous iterations of the satisfy analysis did not account for
-this language feature.
-
-See issue #60789.
-
--- flags --
--min_go=go1.18
-
--- go.mod --
-module example.com
-go 1.20
-
--- a.go --
-package a
-
-type I int
-
-func (I) m() {} //@rename("m", M, mToM)
-
-func _[P ~[]int]() {
-	_ = P{}
-}
-
--- @mToM/a.go --
-package a
-
-type I int
-
-func (I) M() {} //@rename("m", M, mToM)
-
-func _[P ~[]int]() {
-	_ = P{}
-}
-