It is unlikely to matter.
First, unless you have a terribly unique name, it is pretty common for two people to have the same name. I have a pretty good Google presence but there are at least two other people named Justin Cave that come up on the first page of Google results. People generally aren't going to assume that the criminal A Watkin is the same as you.
Second, since this person was convicted of a serious felony, they're presumably going to be spending some time in jail and that conviction is going to show up on a background check. Unless you happen to have been unemployed during the window that this person was in jail, potential employers are going to figure out pretty quickly that you are two different people. And when your background check comes up clean, they'll be assured that you're someone else.
You can certainly work to improve your online presence and you can include relevant links on your resume/ LinkedIn to your online resources. The first page of Google results will almost certainly still include the information about the criminal, though, so you likely want to help people avoid the need to Google your name in the first place. Most employers won't bother searching on your name if you provide them links to follow. It appears that you are a developer so including a link to your LinkedIn profile, a GitHub account with some code samples, a StackOverflow account where you've answered some questions, or a blog that has some technical content would all be appropriate. If you make it easy for a potential employer to get the information they're after, they're much less likely to bother going to a search engine in the first place.