Samsung is Verizon's customer here. Verizon asked them to put the logo on there and Samsung agreed to do it. Do you really think there was any hesitation by Samsung or that Verizon forced them to do it? Of course not, it was a mutual business agreement that benefits both parties, simple as that. If you don't like it, don't buy it. Move on.
everything you wrote is flat out wrong!
for starters, its verizon that's samsung's customer, not the other way around
second, everything else you wrote is useless given that you arent privileged to any internal negotiations between the two companies. This is all in addition to the fact that samsung in no way benefits by having another company's logo on their product. Furthermore, your use of a phrase such as "mutual business agreement" indicates that you have no formal or practical business experiences and thus are in no position to make assumptions as to the practices of major corporations.
Now, since there seems to be a lot of clueless individuals let me elaborate:
Its more than just a logo, its indicative of the carriers bargaining position in comparison to the manufacturer. No other carrier had their logo printed on the home button, this indicates that it was done at the request of Verizon. In order for Samsung to undertake the cost and added time needed to do so, there must have been something to motivate them to do so, and the only logical thing is that Verizon probably would have refused to carry the device had they not done so.
Furthermore, in keeping with the notion that it is a disadvantage to have the carrier have such a strong negotiating stance, consider this;
Verizon's model is the only one (to my knowledge) to ship with a locked bootloader, thus severely limiting one's ability to install custom roms. This is a far more functional limitation than a logo on a button but it stems from my complaint that verizon has too much power over OEMS.
We are also likely to be effected in regards to future updates, since Verizon is likely to exert more influence into what the updates contain and when they are pushed out.
Bottom line, its more than just the logo, and if you can't understand that this problem encompasses more than just a printed logo than you shouldn't be commenting on the issue.
This goes beyond just the Note 2, its about Verizon's anti-consumer business practices in general