Know-How Exchange : Branding

It depends.

Same logo sometimes works. Chevrolet sells all their different model cars under the Chevy logo.

New logo sometimes works. Cadillac and Chevrolet have different logos, even though they are under the same parent company.

Third option of making a new logo related to the old logo also sometimes works. Think how all the Microsoft product icons and logos (Excel, Word, etc.) look similar.

Provide some more information about your situation and we might be able to guide you better. Is the current logo for the company or the product? Will the new product be closely related to the old product? Will the same people be buying both products? Things like that we wold need to know to be able to better answer this question.

Peter's comments are exactly right (as usual).

The rule of thumb, in my opinion, ought to be that if the target audience or the core positioning benefit is different then there should probably be a new name (and logo) to avoid confusion and to give each brand its best shot at establishing a clear image among its audience.

I'm sure there are exceptions, but I'm hard pressed to think of many. Perhaps sub-brands can make sense -- as in the Chevrolet example. Each sub-brand carries the family name and logo along with its own.

If you could provide more information it would be beneficial.
Are these products similar?
Do they both serve the same purpose but to a different demographic? ie: one for adults the other for children but working towards the same purpose. Toys R Us for children 2years and older, Babies R Us for babies and expecting Moms.

If this is the case you can use the same conceptual design but make modifications to reflect the difference. This way the brands are associated but there is a differentiation of them