Is there a way to relabel the domain of a permutation group?

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I could not find such a method, b ut you can use the generators of your permutations group as follows:

sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
sage: G
Permutation Group with generators [(3,4), (1,2,3)(4,5)]

sage: d = {1:'a',2:'b',3:'c',4:'d',5:'e'}

sage: H = PermutationGroup([[d[i] for i in g.tuple()] for g in G.gens()], domain=d.values())
sage: H
Permutation Group with generators [('c','d'), ('a','b','c')('d','e')]
sage: H.domain()
{'a', 'b', 'c', 'd', 'e'}
sage: H.random_element()
('a','d','b','c')
sage: H.random_element()
('a','c')('b','d','e')