diff --git a/lib/src/Uncertainty/Process/openturns/GaussianProcess.hxx b/lib/src/Uncertainty/Process/openturns/GaussianProcess.hxx
index f6e6792237b..1328eef244f 100644
--- a/lib/src/Uncertainty/Process/openturns/GaussianProcess.hxx
+++ b/lib/src/Uncertainty/Process/openturns/GaussianProcess.hxx
@@ -68,7 +68,7 @@ public:
   void setTimeGrid(const RegularGrid & timeGrid) override;
 
   /** Set sampling method accessor */
-  enum SamplingMethod { CHOLESKY, HMAT, GIBBS };
+  enum SamplingMethod { CHOLESKY, HMAT, GALLIGAOGIBBS };
   SamplingMethod getSamplingMethod() const;
   void setSamplingMethod(const SamplingMethod samplingMethod);
 
diff --git a/lib/test/t_GaussianProcess_std.cxx b/lib/test/t_GaussianProcess_std.cxx
index c734d4f49fe..2ccc2f1b5f2 100644
--- a/lib/test/t_GaussianProcess_std.cxx
+++ b/lib/test/t_GaussianProcess_std.cxx
@@ -61,7 +61,7 @@ int main(int, char *[])
     fullprint << "is stationary? " << myProcess1.isStationary() << std::endl;
     myProcess1.setSamplingMethod(GaussianProcess::CHOLESKY);
     fullprint << "mean over " << size << " realizations=" << myProcess1.getSample(size).computeMean() << std::endl;
-    myProcess1.setSamplingMethod(GaussianProcess::GIBBS);
+    myProcess1.setSamplingMethod(GaussianProcess::GALLIGAOGIBBS);
     fullprint << "mean over " << size << " realizations=" << myProcess1.getSample(size).computeMean() << std::endl;
 
     /* With constant trend */
@@ -71,7 +71,7 @@ int main(int, char *[])
     fullprint << "is stationary? " << myProcess2.isStationary() << std::endl;
     myProcess1.setSamplingMethod(GaussianProcess::CHOLESKY);
     fullprint << "mean over " << size << " realizations=" << myProcess1.getSample(size).computeMean() << std::endl;
-    myProcess1.setSamplingMethod(GaussianProcess::GIBBS);
+    myProcess1.setSamplingMethod(GaussianProcess::GALLIGAOGIBBS);
     fullprint << "mean over " << size << " realizations=" << myProcess1.getSample(size).computeMean() << std::endl;
 
     /* With varying trend */
@@ -81,7 +81,7 @@ int main(int, char *[])
     fullprint << "is stationary? " << myProcess3.isStationary() << std::endl;
     myProcess1.setSamplingMethod(GaussianProcess::CHOLESKY);
     fullprint << "mean over " << size << " realizations=" << myProcess1.getSample(size).computeMean() << std::endl;
-    myProcess1.setSamplingMethod(GaussianProcess::GIBBS);
+    myProcess1.setSamplingMethod(GaussianProcess::GALLIGAOGIBBS);
     fullprint << "mean over " << size << " realizations=" << myProcess1.getSample(size).computeMean() << std::endl;
   }
   catch (TestFailed & ex)
diff --git a/python/src/GaussianProcess_doc.i.in b/python/src/GaussianProcess_doc.i.in
index 81e7276e188..b23711ceaef 100644
--- a/python/src/GaussianProcess_doc.i.in
+++ b/python/src/GaussianProcess_doc.i.in
@@ -98,7 +98,7 @@ Available parameters are :
 
   * 1 (GaussianProcess.HMAT) : H-Matrix method (if H-Mat available)
 
-  * 2 (GaussianProcess.GIBBS) : Gibbs method (in dimension 1 only)
+  * 2 (GaussianProcess.GALLIGAOGIBBS) : Gibbs method (in dimension 1 only)
 
 "
 
@@ -113,7 +113,7 @@ Available parameters are :
 
   * 1 (GaussianProcess.HMAT) : H-Matrix method (if H-Mat available)
 
-  * 2 (GaussianProcess.GIBBS) : Gibbs method (in dimension 1 only)
+  * 2 (GaussianProcess.GALLIGAOGIBBS) : Gibbs method (in dimension 1 only)
 
 Parameters
 ----------
diff --git a/python/test/t_GaussianProcess_std.py b/python/test/t_GaussianProcess_std.py
index eab1e2c0ab9..d7dff04890b 100755
--- a/python/test/t_GaussianProcess_std.py
+++ b/python/test/t_GaussianProcess_std.py
@@ -29,14 +29,14 @@
 myProcess1.setSamplingMethod(ot.GaussianProcess.CHOLESKY)
 print("mean over ", size, " realizations = ",
       myProcess1.getSample(size).computeMean())
-myProcess1.setSamplingMethod(ot.GaussianProcess.GIBBS)
+myProcess1.setSamplingMethod(ot.GaussianProcess.GALLIGAOGIBBS)
 print("mean over ", size, " realizations = ",
       myProcess1.getSample(size).computeMean())
 
 # With constant trend
 trend = ot.TrendTransform(ot.SymbolicFunction("t", "4.0"), myTimeGrid)
 myProcess2 = ot.GaussianProcess(trend, myCovModel, myTimeGrid)
-myProcess2.setSamplingMethod(ot.GaussianProcess.GIBBS)
+myProcess2.setSamplingMethod(ot.GaussianProcess.GALLIGAOGIBBS)
 print("myProcess2 = ", myProcess2)
 print("is stationary? ", myProcess2.isStationary())
 print("mean over ", size, " realizations= ",
@@ -50,7 +50,7 @@
 myProcess3.setSamplingMethod(ot.GaussianProcess.CHOLESKY)
 print("mean over ", size, " realizations = ",
       myProcess3.getSample(size).computeMean())
-myProcess3.setSamplingMethod(ot.GaussianProcess.GIBBS)
+myProcess3.setSamplingMethod(ot.GaussianProcess.GALLIGAOGIBBS)
 print("mean over ", size, " realizations = ",
       myProcess3.getSample(size).computeMean())
 
@@ -68,7 +68,7 @@
 
 # Create the "Gaussian Process" discretized on a singleton
 myProcess = ot.GaussianProcess(covModel, mesh)
-myProcess.setSamplingMethod(ot.GaussianProcess.GIBBS)
+myProcess.setSamplingMethod(ot.GaussianProcess.GALLIGAOGIBBS)
 size = 1000
 sample = ot.Sample(size, 1)
 for i in range(size):
@@ -99,7 +99,7 @@
       sample.computeMean())
 print("variance over ", size, " realizations = ",
       sample.computeVariance())
-myProcess4.setSamplingMethod(ot.GaussianProcess.GIBBS)
+myProcess4.setSamplingMethod(ot.GaussianProcess.GALLIGAOGIBBS)
 sample = myProcess4.getSample(size)
 print("mean over ", size, " realizations = ",
       sample.computeMean())
@@ -116,7 +116,7 @@
       sample.computeMean())
 print("variance over ", size, " realizations = ",
       sample.computeVariance())
-myProcess5.setSamplingMethod(ot.GaussianProcess.GIBBS)
+myProcess5.setSamplingMethod(ot.GaussianProcess.GALLIGAOGIBBS)
 sample = myProcess5.getSample(size)
 print("mean over ", size, " realizations = ",
       sample.computeMean())