I would say Grout was probably his mother's maiden name.
His World War I draft card shows he was born September 6, 1890 in Susquehanna County. The town name is hard to read.
He appears with his parents Curtis and Emily in the 1900 census. Emily who was born May 1868 in NY. Coincidentally an Emily Groat age 13, born in NY is listed as the step-daughter to Andrew Carson of Middletown, Susquehanna County in the 1880 census. His wife is Phebe who was also born in NY. Whether Andrew Carson was related to the Corson Family is a good question.