gh-40110: Fix "NotImplementedError: an immutable graph does not change name"
    
Certain methods related to TSP (Travelling salesman problem) fail on
immutable graphs:

```sage
sage: Graph('EJ~w', immutable=True).longest_cycle().order()
NotImplementedError: an immutable graph does not change name

sage: graphs.ChvatalGraph().copy(immutable=True).is_hamiltonian()
NotImplementedError: an immutable graph does not change name
```

This PR fixes this by setting the `_name` attribute directly instead of
setting it via [`name()`](https://doc-develop--sagemath.netlify.app/html
/en/reference/graphs/sage/graphs/generic_graph.html#sage.graphs.generic_
graph.GenericGraph.name).

Another fix would be to allow changing the name of immutable graphs by
removing these two lines from `name()`:

```py
if self.is_immutable():
    raise NotImplementedError("an immutable graph does not change name")
```

This check was introduced in #15681 and [has bitten us in the past](http
s://github.com/sagemath/sage/commit/82f6e161dfedebdc31d09f507a0686f5bf15
c10a). While it seems counterintuitive for *immutable* graphs to have
mutable attributes, the `_embedding` attribute can already be mutated
via `set_embedding()`.

### 📝 Checklist

- [x] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.
    
URL: #40110
Reported by: Lennard Hofmann
Reviewer(s): David Coudert

Author: Release Manager

src/sage/graphs/generic_graph.py

@@ -8410,6 +8410,9 @@ def longest_cycle(self, induced=False, use_edge_labels=False,
             True
             sage: D.longest_cycle(induced=False, use_edge_labels=True, immutable=False)[1].is_immutable()
             False
+            sage: # check that https://houseofgraphs.org/graphs/752 has circumference 6:
+            sage: Graph('EJ~w', immutable=True).longest_cycle().order()
+            6
         """
         self._scream_if_not_simple()
         G = self
@@ -8565,7 +8568,7 @@ def F(e):
                     hh = h.subgraph(vertices=c)
                     if total_weight(hh) > best_w:
                         best = hh
-                        best.name(name)
+                        best._name = name
                         best_w = total_weight(best)
 
                 # Add subtour elimination constraints
@@ -9304,7 +9307,7 @@ def hamiltonian_path(self, s=None, t=None, use_edge_labels=False,
             return (0, None) if use_edge_labels else None
 
         tsp.delete_vertices(extra_vertices)
-        tsp.name("Hamiltonian path from {}".format(self.name()))
+        tsp._name = "Hamiltonian path from {}".format(self.name())
         if immutable:
             tsp = tsp.copy(immutable=True)
 
@@ -9579,7 +9582,7 @@ def weight(label):
                                  (vv, uu, self.edge_label(vv, uu))]
                     answer = self.subgraph(edges=edges, immutable=self.is_immutable())
                     answer.set_pos(self.get_pos())
-                    answer.name("TSP from "+self.name())
+                    answer._name = "TSP from "+self.name()
                     return answer
             else:
                 if self.allows_multiple_edges() and len(self.edge_label(uu, vv)) > 1:
@@ -9589,7 +9592,7 @@ def weight(label):
                         edges = self.edges(sort=True, key=weight)[:2]
                     answer = self.subgraph(edges=edges, immutable=self.is_immutable())
                     answer.set_pos(self.get_pos())
-                    answer.name("TSP from " + self.name())
+                    answer._name = "TSP from " + self.name()
                     return answer
 
             raise EmptySetError("the given graph is not Hamiltonian")
@@ -9738,7 +9741,7 @@ def weight(label):
             # We can now return the TSP !
             answer = self.subgraph(edges=h.edges(sort=False), immutable=self.is_immutable())
             answer.set_pos(self.get_pos())
-            answer.name("TSP from "+g.name())
+            answer._name = "TSP from "+g.name()
             return answer
 
         #################################################
@@ -9810,7 +9813,7 @@ def weight(label):
             f_val = p.get_values(f, convert=bool, tolerance=integrality_tolerance)
             tsp.add_vertices(g.vertex_iterator())
             tsp.set_pos(g.get_pos())
-            tsp.name("TSP from " + g.name())
+            tsp._name= "TSP from " + g.name()
             if g.is_directed():
                 tsp.add_edges((u, v, l) for u, v, l in g.edge_iterator() if f_val[u, v] == 1)
             else:
@@ -24896,7 +24899,7 @@ def is_hamiltonian(self, solver=None, constraint_generation=None,
 
         TESTS::
 
-            sage: g = graphs.ChvatalGraph()
+            sage: g = graphs.ChvatalGraph().copy(immutable=True)
             sage: g.is_hamiltonian()                                                    # needs sage.numerical.mip
             True