Although a political party should involve certain degree of flexibility, changing the name in order to create identification in its supporters might undermine its credibility, showing an undesired bias, similarly to what would happen if the party decided to adjust its ideology to please any of their members, because this would show a simple strategic interest.
On the contrary,if they push an ideology which might satisfy its counterpart, it would build up its credibility by allowing enough room for the political debate, so the answer is C.