Should a Buddhist feel offended by misuses of Buddha's name or image? I have just found out that there is a person producing and selling a beer in my town called "Buddha Beer" with Hotei's picture on it.

Initially I found it offensive and disrespectful (marketing Buddha's name, associating it with alcohol and putting the image in the trash just like every bottle when it's empty). Well, I'm sure the person meant no disrespect, I know the producer, but I still didn't like it.

Allow me to give more context: We live in a country with almost no Buddhism in it. People have no idea regarding what Buddhism is all about and commonly confuse the Buddha with Hotei.

Even though the person meant no disrespect I found it disrespectful and so this question came to my mind: If I felt offended by it, is this a problem that I have with attachment? So, where is the real problem, in the beer or in myself? Or maybe in both?

I thought about talking to the person and explaining why this is a bad idea but I'm sure it will be completely useless (let's face it, no one will change a brand because of that as the commercial impact is irrelevant here and people dont believe in Kamma) and I will also look like "that boring guy" that complains because of religion. I guess I will do nothing unless someone asks for my opinion.

That said, how a Buddhist should behave in such a situation. Shoud we feel offended? Should we discuss it with someone not Buddhist?
What would be your plan of action, if you saw someone running a brothel with your mother's name and picture on it? Feeling angry or not depends on if you have eradicated anger. You can do Metta meditation to deal with your anger. But that doesn't mean it is wrong to take action against such establishments, even if they mean no disrespect. There's nothing wrong in peacefully protesting, trying to make them come to their senses or using any legal options available. You don't actually have to get angry while doing it. You are doing them a favor since they are committing bad Karma due to their ignorance. Buddhists don't always have to accept people's ignorant acts meekly in the name of Metta.

Once there was this cobra practicing loving-kindness in the forest saying: May all beings be well, may all beings be happy, may all beings be peaceful. And an old woman who was collecting firewood saw this cobra and mistook it for a rope. So she used it to tie up the firewood that she was carrying. As the cobra was doing loving-kindness practice, it allowed this woman to do anything. So after the woman carried the bundle of firewood home, the cobra escaped, but with a lot of wounds and physical pain. So he went to meet his teacher who was the hermit(Bodhisatta) staying in that forest. The cobra said: See what happened to me! I was practicing loving-kindness, and now see the wounds and all the pain that I'm experiencing in my body! The teacher very calmly said: You have not been practicing loving-kindness. You have been practicing idiotic compassion, because you should have shown that you were a cobra. You should at least have hissed! So with regards to people like the person you've described, you have to learn to hiss, and in doing so you'll also be doing a service for that person.

So if you have any crowd pull, go hiss without biting. :) Or use social media to protest and let them know about it. If business owners get the idea that whenever they do something like that, there will be negative consequences, they will be reluctant to do it in the future as it is bad for business.