I already have my business up and running. I am getting a lot of negative response because of the business name "Dude Undies". Now its like starting over from the beginning and I have no clue on another name. Mind you I only have 1 week to either renew the name or pick another business name.
To get started, I'd like to understand why you only have a weeks time to make a decision? Also, what do you mean when you say *renewing* the name? I believe, you, once again, are in haste and may be you should slow down a bit to take stock of the situation. Rebranding has always been expensive (Time, Effort, Energy, Capital) and will be like so in future as well. Don't make the same mistake twice.
Can you help me understand the approach you took last time to conclude with "Dude Undies" and how'd you wanted to position the business?
Coming back to your question "What's the best way of coming up with business name ideas", just start with a simple fact that renaming isn't some form of satanic activity. Many companies have done that successfully in the past (FedEx, Sprint, Uptivity, etc). You should rather get bothered with whether you, or anybody else in your team, carry adequate knowledge on naming a business.
To help you further, you can chose to:
1. Keep the transition uniform and planned. You would need to communicate the change for some times to come.
2. Brainstorm & taste the test or test the taste. Salt is always salty, but you need to know the right quantity per specific dish.
3. Think about the activities that you would need to run in parallel.
Is there anything specific you're looking at? Feel free to receive with more clarity to get clarity. I am just a buzz away. All the best!!