Hi, I hope this is the right place to post this.
I run a transport and home moving business, which has existed since 2014, currently operating in one city, with plans to expand to others.
I have an IT background and have done quite a bit of research into SEO over the years, but I'm not sure what to do now and I'm hoping you guys can advise.
The domain name I have is exactly the name of my business and is 5 characters + TLD. I've had this domain since I started the business.
I quite like having a short domain name and have structured my URLs to be short such as /about/ and /reviews/ and would continue this if I expand to other cities such as domain.tld/cityname
The most popular search phrase for me is 5 words long and in recent years I've ranked between position 4 and position 8 for this phrase.
Most of my competitors who rank above me have called their business something that contains most of the words in this popular search phrase, in various orders and have a domain name to match, but none of them match the phrase exactly.
I've managed to buy the domain name that exactly matches this search phrase (searchphrase.com) but the question now is, what do I do with it?
I don't want to change the name of the business to match this new domain because I have significant brand recognition (5 times as many click throughs as for the popular search).

I'm considering linkbuilding with the new domain, and redirecting it to the old one. Do you think this is likely to help, or will Google penalise me for this behaviour?
It seems my other options are:
Move my site to the new domain, and keep the same business name
Build a separate site as a new brand of the business on the new domain, and linkbuild for that

Thanks for reading. Any thoughts on the best way to capitalise on having this domain gratefully received.