I don’t completely disagree with @Aishah Mustapha , but I think it is a limited answer. The problem as a startup venture you don’t always have all the answers figured out before you start doing business. I’ve been a beta tester of many services that changed after some initial traction. One was called Mogulus (a live streaming company back around 2008) they later transitioned from individual creators to businesses and large events and rebranded as LiveStream. Another one was an online course creator that started out as With Coach, it later became Podio. As my examples show one went from Abstract to literally saying what their service is and the other went from being straight forward to being a bit more abstract (the thinking was that Podio is similar to Podium).

I agree that if you execute well it doesn’t matter so much what your name is, but it can have implications that impact the rest of your brand. Some names are easier to brand around than others, but that may not be known at the beginning. Also if your products, services or customers change than perhaps it is worth revisiting your business name.

It is also vital to understand your customer base. Many fashion brands (especially luxury ones) typically use some version of the founder’s name or initials. This type of choice can also determine or help drive your branding colors, font choice, imagery, price point of product or services and more. Another example is the sun lotion brand Sun Bum, they have playful colors, a playful gorilla mascot, and do lots of ads with surfers. However, Apple is sleek and serious but wants to show you that it doesn’t look or function like other similar brands and its prices follow that.

I would dissuade you from using a name generator if you are ever interested in trying to trademark or protect your name and logo. You need to do some serious thinking and research to understand if the name you want is already in use to give you a jump start on protecting your intellectual property as well as avoiding lawsuits from similarly named ventures (locally, regionally, nationally, and even internationally).

There is no rule for this, as we are entering the world of 'animal spirits' to use an economist term, I've seen rubbish name work well and good names fail. Not to dismiss the importance of a name, it can shape one's whole business success.

One camp, is to go with the first name, as it'll be the best.

Another, risk avoidance camp, is to use a systematic approach from a list appropriated that explores 21 variables, try to end up with at least 20 names to eliminate. From here, get it down to three "heroes" that are not trademarked and tools don't own the domain. Good luck with that headache! 

Those successful three need to be processed further. Make business cards and collateral to visualise the name, sleep on it. Can you live with it, for it to be part of one's identity.  Try to avoid "decision by committee" as one needs experts here. 

Like all things creative, it is better to hire an expert. When one considers the hundreds of thousands and thousands of hours spent building a business, saving a few thousand on critical assets like this may be "false economics".

What’s in a business name? Not too much if you execute well, and there is a need in the market for your product or service. Having said that, coming up with a good business name can help your marketing. It involves going down to the essence of your brand.
 
What is your business’s purpose? What problem are you solving? How do you want to make people feel when they hear your name? Those are good starting points. Refer to competitors in your industry by looking at their name, tagline, values or motto. Try to understand why they resonate with customers.
 
Next, you can use business name generators. There’s plenty but the best I’ve found is namelix.com
It even generates logos for you and checks if the domain name is available for that name.
All you have to do is put in a few words you want your brand to be associated with and it uses AI to generate a unique name. It’s quite fun to play around with.