Different e-mail name than group name

Is it possible to have a different e-mail name than the group name.

In our company we create o365 groups for every engagement. We put the engagement code in our group name. In some engagement we use the office 365 e-mail for external communication. We adapted the e-mail address but when we cc our group mailbox, the group name shows up. Is there any way to change this for the e-mail part only without renaming the entire office 365 group?

Thanks