On the 2016 list of top names from the SSA, Oliver came in as the 12th most popular boy's name. While that's high, and the name has been on a sharp increase in recent years (as recently as 2008 it wasn't in the top 100), that's still lower than in many other Anglophone countries where it's at or almost at the very top of the list. What's the reason people in the States haven't been quite as keen on picking up this fashionable English classic? There may be several factors in play here, but one major one may not have to do with Anglo-Americans' tastes, but rather another culture that makes up a growing part of the U.S. population diluting the stats.
That culture is the Hispanic/Latino population of the U.S. Some other name bloggers have mentioned how that population has influenced the American baby name stats, both with names popular in both cultures (e.g. Isabella and Sophia/Sofia) and with distinctly Spanish names (e.g. Joaquin) (all those examples are mentioned at the above link). On the other hand there are names which are common among English speakers but not among Spanish speakers; the name this post is about, Oliver, appears to be one of them.
With the SSA state-by-state stats just released on the day I'm writing this post, if you compare the stats of states with high Hispanic populations vs. those with low Hispanic populations this pattern emerges. Many of the less-than-average-Hispanic states do have Oliver in the top 10, with some at or almost at the top. On the other hand, Oliver does worse than average in states like California, Texas, and Florida (heavily Hispanic states).
What does this mean if you're an American with a son (or are planning on having a son) named Oliver? In terms of the odds of him sharing a name with a classmate, it's probably more likely if most of his schoolmates speak English and less likely in a more diverse bunch (this contrasts to other "international" names, such as those mentioned in the second paragraph, which are popular in multiple cultures and are more likely to be heard where there are people from a wide variety of ethnicities). As for the practical effects, giving him a decidedly Anglo name like Oliver will likely be a plus when it comes down to potential "name discrimination" - but a greater risk of spelling/pronunciation issues when interacting with Hispanics, etc. than for example a more "Spanish-friendly" name.