According to what is stated on this site, there was only one Oliver P. Beck, which served briefly in Arkansas, but primarily in Missouri.

http://www.couchgenweb.com/civilwar/27infcoh.html

Twenty-seventh Regiment Arkansas Infantry.
Company H.

BECK, OLIVER P (Oliver Perry Beck)
Third Lieutenant—Enlisted in Izard county, Arkansas, June 14, 1862; age 32, born in Indiana; resigned, August 23, 1862; subsequently served in 3rd Missouri Cavalry.