Naming creative projects is tough enough to begin with, now add 7 billion human beings and a century of increasingly diverse and productive music production and you've got a recipe for name conflicts and shortages. Obviously the best thing to do is pick something completely unique that has zero results on Google (and doesn't sound like any other artist after you account for non-standard spelling). Failing that, picking a name not used in your target genre/market might be acceptable, if the other entity with your name is not too well known in theirs... but in general, as soon as you are mucking around with names that have been widely used, you're asking for trouble. Do your research, check and double check. Or at the very least look into a dictionary to avoid silly mistakes (ahem, Bizzare Contact).
On the other hand, even those of us with well-established identities will sometimes have problems... I've been "Basilisk" for 20+ years but I'm far from the only one. Luckily the others are mostly metal bands or doing electro-industrial or something not very related to what I'm known for... but in the last several years a new Basilisk has emerged in Germany, playing mostly hard techno, but often appearing on line-ups at psytrance-adjacent events... I've spoken with him at length and he's been very disrespectful about the whole situation, but I'm not about to abandon an identity I've had for so long... guess I'll just have to beat him at his own game, huh? Sometimes your best option is just to compete in the marketplace of ideas and artistic expression.
As an aside, Beatport has been doing something a little peculiar as of late: throwing the country of origin into the names of artists with conflicting names... so now you've got Mohn and Mohn (NL), for example... and since that's the actual name listed on Beatport, this same info ends up in Discogs, and in some extreme cases I've even seen artists adopt these modifiers as their official names on SoundCloud, Facebook, etc.!