They managed this trick easily enough because they had already established that the figure of Robin Hood was a role designated by a figure out of English myth, Herne the Hunter. While the original myth says that on the twelfth day after the Winter Solstice Herne gathered his hunt at an oak tree in Windsor Park in England and rode the sky seeking prey (I don't know if it still stands but there was an oak tree on the grounds of Windsor Castle known as Herne's or The Hunter's Tree), for the television show they've made him into more of a mixture of a few figures from pagan times: the Greenman, the Stag King, and Herne the Hunter. In both the first episode of the series, and the opening episode of the third season, the characters played by Michael Praed and Jason Connery are designated by Herne as his son, and the person to carry on the fight against the Saxons using the name of Robin of the Hood.
As with everything else about the series, the situation was handled neatly and cleanly. It may sound a little contrived on the page, but in the context of what had been established in the previous two episodes it worked. Unfortunately Jason Connery lacked the charisma of Michael Praed and, in spite of doing some fine work, never seemed to capture people's imaginations and the series ended after the third season. If he had been cast as Robin from the beginning Connery would have been a fine choice, but Praed had made the role so much his own that anybody would have paled in comparison.
There's also a noticeable drop-off in the quality of the scripts from the first two seasons to the third. Part of the problem is just how many variations on the theme of keeping out of the clutches of the Sheriff of Nottingham, embarrassing his lackey Sir Guy of Gisbourne, and robbing from the rich to feed the poor can there be? In the first two seasons they were able to draw upon the adventures attributed to Robin Hood in various books, including many of the old favourites like his meeting with Little John, and give them new twists to create interesting episodes, but the scripts seemed to lose direction somewhat in the third season.