Here’s a screencap showing the ‘sail number’ / hull number of the Red October:
Hard to see and easy to miss on a small TV screen, here it is: ВМФ СССР 436.
Here’s the translation from Wikipedia: Военно-морской флот СССР (ВМФ); Voyenno-morskoy flot SSSR (VMF), literally “Military Maritime Fleet of the USSR.” Not much different from writing “US NAVY” on a sub. I don’t know if ‘436’ has any special significance.
Couldn’t find a font that matched exactly (the 4 was particularly problematic), so I had to draw it.