Brand and content strategy both need to be considered, and both are related to UX, and will help to unify product experiences.
Brand manager positions can have fairly large differences in responsibilities depending on the size of the organization. From your description, it sounds like you need to unify the product experiences from their individual silos. This may be one role, or several. Either way, you'll have to consider a couple things to promote shared understanding across the company:
Brand as unifying look and feel: have visual standards.
as @jhurley mentioned, you need clear brand standards, by this I mean primarily visual standards.
Mailchimp is thorough on this (NOTE: I don't work for Mailchimp; I have just had great experiences as a customer).
Even though this is the presentation layer, they consider this part of the UX (some companies silo their visual designers a bit); it's even in the URL: https://ux.mailchimp.com/
Content strategy as unifying voice and tone: have a content styleguide.
How we speak to customers and prospects is the concern here. Once again, Mailchimp considers this part of the UX; they do a brilliant job across their company.
Here's a screenshot showing all the considerations they touch on. If you're trying to unify your product experiences, shared language and tone is essential. It puts both product and communications teams on the same page.
This will help unify the personality that we as one company address our prospects and our users. Are we quirky? conservative? playful? serious?
This will effect everything from error messages to emails to sales pages.