Absolutely! If you have legitimately satisfied your customers, then why shouldn’t you ask them to write a customer review for your business?
As long as you’re doing your job, satisfying customers, giving them a positive experience with your business, then your customers would probably have no problem writing about it.
The important thing to remember with this stuff is to ask for customer reviews tactfully. Don’t just ask every single person who walks into your establishment to write you up.
To return to the party metaphor, this would be like if a new person at a party walked up to every guest and said, “Please like me, please like me, tell all your friends how good I am!” This would be desperate. This party guest would be laughed out of the room, with everyone pointing and saying, “What’s wrong with that guy?”
Asking for a customer review should come about naturally... Talk to your staff about recognizing opportunities to suggest that customers write a review.
If your staff has the right touch, and you train them correctly, the positive reviews should start streaming in.