"Come round to" has several synonyms that can be used interchangeably depending on the context of the sentence. Some of the most common synonyms include "accede," "agree," "assent," "consent," "yield," and "succumb." These words all convey the idea of someone coming around to a particular opinion or viewpoint after initially not being convinced. Additionally, "change one's mind," "alter one's perspective," and "reconsider" are also synonyms that can be used to convey the same meaning. In essence, the synonyms for "come round to" all refer to the act of changing one's opinion or perspective on a particular topic or idea.