Can two logos share one icon?

There is no right or wrong, it depends on the marketing and corporate strategies here. CocaCola uses the same logo as their http://www.coca-colacompany.com/ as on http://www.coca-colacompany.com/brands/coca-cola; and the same logo is on both corporate and product websites. Pepsi hashttp://www.pepsi.com/, and a http://www.pepsico.com/ for corporate. If you think the company will, at least for the next few years, be known primarily for the product in question, a close identification between the two makes sense. It can be changed down the road. On the other hand, if the company intends from the start to pursue a multi-product strategy (which Pepsi does, much more than CocaCola), then keep them separate. Your case is somewhat different in that the product name and company name are quite different. So, using the same graphic icon could cause confusion. On the other hand, it helps to tie the product to the company. So as I said, if the strategy is pretty much single-product, I would go for it.

I agree with beagle that if the company has a single product strategy a close identification is fine. However, keeping product and company logos separate can be useful as a "reputation risk fire break" should the product fail or be on the receiving end of some very bad publicity. Individual graphical design can therefore be a useful marketing risk mitigation strategy.

I seems common to do what the clients is suggesting. Just for example, IBM and Dell and HP have various product lines (Dimension, etc.) with a unique name but they don't have their own logos.

You mean like the way there's a https://www.google.com/search?q=chevrolet+logo&hl=en&tbo=u&tbm=isch&source=univ&sa=X&ei=KQ25UN3lEIWSiAKgm4DwBg&ved=0CC8QsAQ&biw=1920&bih=1019 logo on the https://www.google.com/search?q=chevrolet+logo&hl=en&tbo=u&tbm=isch&source=univ&sa=X&ei=KQ25UN3lEIWSiAKgm4DwBg&ved=0CC8QsAQ&biw=1920&bih=1019#hl=en&tbo=d&tbm=isch&sa=1&q=corvette+logo&oq=corvette+logo&gs_l=img.3..0l6j0i5l4.10701.11828.0.12029.9.9.0.0.0.2.123.706.7j2.9.0...0.0...1c.1.tGSr0ewjL0U&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.&fp=fcb1367a66240493&bpcl=39314241&biw=1920&bih=1019 logo? It can be a good thing if done right.

I would give the example of Motorola. http://www.motorola.com/us, each with the same logo (albeit different colors, although that's not always even the case). So yeah, a good thing if done right.

I would advise using similar elements of the same logo (like Motorola does), but would shy away from making them exactly the same with only the language being different. As beagle points out, that means that OriginalProduct is Company, and when you come out with OtherProduct, it will always be a lesser thing -- both within Company and to consumers.

No offense, but if this company is at the start-up stage or early enough in the game that we're hashing it out on metafilter, they're really overthinking it. As has been pointed out, there are plenty of companies where "corporate" logo more or less equals flagship product, and plenty of examples otherwise. If the product name isn't that of the company, then I think your answer is made for you. You have to design logotype for the product, at least to the extent of creating a distinctive look and feel for the product name. It's fine to make the corporate ID part of that product's trade dress; it doesn't dilute the corporate ID if it's done right. Another cautionary note: I've noticed a tendency, despite anyone's best intentions, for the product names, the thing that people actually USE, to take control rather than the corporate mothership behind it. This is true even when the corporation for whatever reason (only one I can think of is ego) really spends a lot of money to try to brand themselves. I do work for a client where they manage a credential. Let's call the organization ABC and the credential the XYZ certification. I have a lot of conversations like this: "We do work for the ABC organization." "Who?" "They manage the XYZ credential." "Oh yeah! I know 3 guys with the XYZ credential." This despite all kinds of image polishing on the part of ABC. So they should probably spend more time thinking about the product branding than the corporate branding. Just my opinion. YMMV.

They are overthinking, but they've been around a decade with a non-memorable company name and a really crappy logo and I expect they'll be around a long time more regardless. They hope to grow sales of the new product to a 50/50 split between new product-branded doodads and existing company-branded services. They're finally coming around to the idea of an upgrade to put them a little more on par with their much more polished competitors. Whatever we get will be miles better than what we have. I just don't want to see them set up with logos they're going to regret soon. I like the Motorola and Chevy examples, but what the client is suggesting is more like taking the Motorola circle-m from the corporate logo and using it to dot the "i" in the Droid logo. Or taking the Chevy gold bar and interchangeably using the words "Cheverolet" or "Corvette" under it, in different fonts. Seemed to me to be a setup for brand confusion. I would like to see them take the IBM/HP/Dell/AMD approach but I'm losing that battle. Vector and Cutco is probably the best model. Thanks everyone for the ideas.