Hello! This is a good question I think many go through the same phase when launching a business.
My first tip is don't use an acronym such as LGA or MVA for example, acronyms are not memorable. That's what you are looking for, memorable names. With that said, is also important not to get too hung up on a name because a name does not make the brand, although it can definitely help it.

What type of lead generation service are you planning on offering? Digital marketing/lead generation? If that's the case I would assume that you know that SEO plays a big role in lead generation and the linking is a huge factor so if you were to change names and domains later you need to expect to have to relink everything to stay consistent and not have any broken links. I wouldn't recommend waiting but I would try to plan out the phasing accordingly. Maybe consider using your name as the service name.

While I name is important, I would not let it stop the process. You can always market a company with a bad name and build a reputation of great service and products.

There are great companies out there with stupid names. Google, comes to mind. It is a made-up word that we now use as a noun and a verb.

When it comes to names, choose something that is memorable and easy to spell.

Also, it sounds like you are naming a product rather than a company. At this point, focus on the high-quality, consistent deliverable and let the name come later on.

A bad name will cost you money. How? Missed opportunities. I could list a dozen ways.

Changing a name will also cost you money. How? Time. Energy. Redesigning marketing materials. Etc.

I don't know whether your brand name / domain name is good or bad. But it sounds like you're dissatisfied with it.

Think of your brand name like a coworker. Either you "hire" a name that goes out of its way to build your brand and business. Or you "hire" a name that's lazy, doesn't show up, misplaces things, rubs customers the wrong way.

Interview your name before hiring it.