Remove redundant name check when adding QuantumCircuit registers.

qiskit/circuit/quantumcircuit.py

@@ -3636,11 +3636,6 @@ def add_register(self, *regs: Register | int | Sequence[Bit]) -> None:
                 )
 
         for register in regs:
-            if isinstance(register, Register) and any(
-                register.name == reg.name for reg in self.qregs + self.cregs
-            ):
-                raise CircuitError(f'register name "{register.name}" already exists')
-
             if isinstance(register, AncillaRegister):
                 for bit in register:
                     if bit not in self._qubit_indices:

releasenotes/notes/create-register-performance-fe392209793d151f.yaml

@@ -0,0 +1,7 @@
+performance:
+  - |
+    Improves runtime performance of the :py:meth:`~.QuantumCircuit.add_register()` method on
+    :py:class:`~.QuantumCircuit`. Consequently, this change improves performance when
+    creating :py:class:`~.QuantumCircuit` as well. Generally, the time complexity of
+    checking register name presence was reduced to :math:`O(1)` from :math:`O(n)`. This was
+    achieved by removing redundant error checking.