Most of us have no control or say over our name - it was the one given to us by our parents at birth. Some of us use a nickname or are known more by our middle name than our first. Since we literally are trying to make a name for ourselves in business and online, there often are complications that likely were never foreseen when our parents named us. In fact, until the recent popularity of the internet, having a name shared by others (including famous actors, athletes, scientists, public figures, writers, or performers) or a very unusual name wasn't near the issue that it is today.
So, when someone does a google search (or use bing, yahoo, or other search engine), they find several references for the more famous namesake or namesakes but may not find us until page three or later. Sometimes we can get lost in the shuffle altogether. Sometimes, it several pages back before our name appears - depending on how many famous or in-the-news people share it with us. It doesn't even matter who had the name first (as in who is older). It's a matter of visibility and usage.
Our parents probably didn't intentionally name us the same as someone with a recognizable name so that we would have to compete for online recognition with them. In fact, our namesake was likely an unknown in the developmental years anyway, and the internet was tears away also.
It's possible our parents wanted to give us a famous first name from the past that they were fond of, and this may cause some issues with people finding that historical or more famous name rather than ours in an online search. When both our first and last name match a more famous personality, we definitely can get overshadowed online.
The real issue is when someone gains a following because they are a TV or movie actor or other prominent person and they share the same name as us - of we them. They are going to come up first in the searches.
So what's the answer? How do you make a name for yourself when all of the names are the same? Say that your name is Steve Smith - do a search and see what comes up.
It's time to change our name - nothing formal - for marketing an online search purposes. Just add a middle initial (even if it's a "made-up" one because we don't really have a middle name or apply a nickname that we invent). So, we can be Steve (or Steven) X. or Z. Smith (when the X or Z stand for nothing except as a differentiation tool). We can be Steve "Skip" Smith (even if we have never used this name before).
Unless we want to remain buried deep within the searches - sometimes there are 20 or more people on Linked In with the very same name - we need to come up a name modification that will identify us.