Nothing more exciting than because seaguls are associated with the seaside which is where Brighton is situated. Other words which could have been substituted could be 'crappy', 'the team with no stadium,' 'budget'. None of these words passed the initial board meeting when the club was being created so they chose the lesser of 2 evils, i.e. the bird that everyone hates.
Reeperbahn, Reeperbahnm, Reeperbahn. Nothing else needs be said!