First off. How's its bore? (bright or dark?) 25-35 was a common cartridge for the 1894-early 94s. But as of late finding those Saddle Ring rifles in 25-35 has become a challenge for collectors. So those two items alone would add some value to your rifle. As far as what it is worth. Initials carved. Grading its condition at 50%. 650-700 on the high side. Perhaps a little less I'm guessing without having a up-close look myself.
If those initials weren't cut too deep or too large or located in a prime area of its stock. That sure would be helpful. Seldom does anyone find a pristine pre-64 saddle ring rifle these days. So, some dents & dings from use are considered mildly acceptable. Wood whittling or initials carved, on the other hand, no collector cares to see.