It looks like it depends on what country's history you are talking about.
The term I usually hear is "Victorian Era" (or "Victorian Age", or sometimes just "Victorian" as an adjective).
Now technically the literal meaning of this would apply to the years 1837 to 1901, and only to UK history, but you often hear it applied to US history too, particularly when the discussion is centered on morals.
The Victorian era is famous for the Victorian standards of personal
morality. Historians generally agree that the middle classes held high
personal moral standards (and usually followed them), but have debated
whether the working classes followed suit.
I also often hear the term used when talking about other trans-national fields of endeavor that the English may have taken part in, even if the specific actors were not English. This particularly includes science and literature.
If the discussion is centered on US politics, the term generally used is "Progressive Era".
The Progressive Era was a period of widespread social activism and
political reform across the United States, from the 1890s to the
This was preceded by what is commonly called the "Gilded Age".
How these (and the Belle Époque mentioned in a previous answer) are all interrelated is well described in this Wikipedia snippet:
The early half of the Gilded Age roughly coincided with the middle
portion of the Victorian era in Britain and the Belle Époque in
France. It was preceded by the Reconstruction Era that ended in 1877
and was succeeded by the Progressive Era that began in the 1890s.