Building a reputation isn't about constant self promotion and isn't judged on the amount of networking events you attend. Just like any brand, a law firm or lawyers reputation is built on trust. Trust is absolutely essential in client relationships, because your client wants to know that they're in safe hands, and you should be making small everyday-efforts to reassure them of this.

Get to know your client on a personal level (I'm not suggesting you go for long walks in the countryside together, just dedicate a small fraction of your time together to engaging in non-business chat), understand their unique situation, understand how they'd like you to handle their issue rather than assuming - if you make a mistake, recognise you're at fault - and it's likely that your client will be all too happy to share their experience with others.

See, that's how trust works: if others trust that client of yours (family, friends, colleagues) then they will trust you, and that's how your reputation grows.