I'll give you my take: A name doesn't mean a whole lot in and of itself but it potentially can.
Let's pick a couple of examples:
Microsoft. We all know Microsoft is huge and as such, it has some really smart and hardworking people but it must also have some jerks, lazy people, and not-so-smart people who snuck in. Anyone who has a decent amount of life experience knows that any organization of large size doesn't have all geniuses or all nice people. Period. So simply stating you worked at Microsoft to me personally doesn't quite cut it. However, if I look you up and I see some awesome contributions you've made, you had a great reputation, you're nice, AND you worked there, that's a win.
Now, let's discuss a more specialized field like cryptography. Say I need a crypto expert and I see that you've worked at RSA - the firm who created the RSA algorithm used on billions of machines and transactions today... I'm thinking "ok, this is good." I look at how long you worked there, you spent 10 years there. Well, my thought is now "Ok this person has spent 10 years working as a cryptographer for some of the best and most successful cryptography experts in the world." I have a good opinion of this. If the rest of my research on you lines up and you're a pleasant person, this is good.
Now, if you worked for either of those, have little work to show, can't explain what you've done, and/or have a bad reputation as being a jerk... That's different. That's my thought process.