No. You generally only need to provide a citation if you mention a character’s name in a summary of the work (or portions of it) or if you are quoting a character’s speech. You do not need to cite the work each time you mention the character as part of your analysis. In the following example, the first sentence requires a citation, but the second sentence does not:
While sitting outside with Mary Crawford, Fanny remarks, “Every time I come into this shrubbery I am more struck with its growth and beauty” (Austen 143). In making this observation, Fanny demonstrates that she is sensitive to the natural world.
Austen, Jane. Mansfield Park. W. W. Norton, 1998.
Published 9 January 2020