I think that using different brands for products and services makes sense if your organization has a very clear division between the product and service parts and you have no gains joining that parts, like getting cross-selling or upselling.

In that case I would use a single brand for the services and another one for the product divisions. In the end they will be different business units with their own budget, right?

For instance, support will be very different for one kind of business than the other.

...Anyway...

DO use different branding -at least a minimal one- for all products just for discoverability. I mean, every product should have its website (like a brochure) and might have a blog, twitter account, facebook page, and so on. Use that accounts for _minimal_ stuff like announcing bugfixes or new releases. If the product goes well, invest in marketing (hire or buy) but it's very important to secure the social assets now.