There are several synonyms that can be used in place of "become associated." One option is "form a connection," which implies the creation of a link or bond between two people, ideas, or objects. Another option is "establish a relationship," which suggests the development of a connection or bond over time. "Forge an alliance" can also be used, indicating the formation of a partnership or collaboration. "Develop an affiliation" or "build a rapport" are additional options for expressing the idea of becoming associated with someone or something. Ultimately, the choice of synonym will depend on the context and tone desired.