Keep Marketing on one side and tell me through which other mean you will tell other people that you're good in your work. This is the only way to tell with a proof.
I don't think there's anything wrong with asking clients to review your service or to suggest where. Suggesting where simply saves them the time of looking for a place to do it. Suggesting a tone or offering compensation is too far. But nothing wrong with "hey, google reviews are super impactful for us, if you get a moment to leave a word about the service, that would be great!"
For me, it is good if customers will leave a feedback about your services. But it is not necessary to ask them, it's up to them if they like. You could just put it at the end of your services, like what they just said 'signature'. Make sure that your signature is readable and highlighted.
Asking directly won't be a good idea.
As mentioned earlier, you can add a link in signature. This will give your customer an option to opt out if he don't want to review.
You can ask feedback if you have given any exceptional solution and the client is very happy. But this is allowed only occasionally.
In other cases, direct asking is never appreciated.