My 2 cents - sure if it's available and the government will register it to you then you own it. Unless you have a trademark they are actually probably free to keep using the name. It may create some confusion for both of your customers. Could be good - could be bad... a name is overrated.
I think a great business (takes care of customers, reliable, honest) will thrive even with a boring or "bad" name but some catchy sounding name that doesn't actually deliver will not last long.
So my point is - the name doesn't much matter so long as it isn't offensive and potentially lends itself to describing your product or service... (doesn't always have to)
If you’re low on start up cash and low on experience as a new entrepreneur I recommend checking out r/flipping - it’s a subreddit about buying things (from fb marketplace, yard sales, thrift stores, estate sales, etc) and reselling them for higher on eBay or Mercari, etc.
It’s a good way to learn about buying, selling, cash flow, customer service, etc., and the barrier to entry can be low like $25-50 low to get started.