When rendering an animation in Blender, the file name will have the frame number appended with four padded zeros as per the documentation.
Can I insert an offset here? I am rendering an image sequence and need the file names to start at name-0011.jpg. The result I am getting now is name-00110001.jpg, name-00110002.jpg etc.
As time goes on, I will need the file names to start at higher and higher numbers. I can't change the start frame because then I won't get the whole sequence rendered, or?
When blender automatically adds numbering to the output filename, it will always use the current frame. The numbering will be in addition to any numbers you may have in your base filename, you can place one or more # in the filename as a placeholder for the frame number.
There is no reason you can't start and end an animation at any frame you want, using frames 25-63 or 35264-35278. Blender does have a maximum frame number which is greater than one million.
You can easily move an existing animation to start at another frame, either the dopesheet or graph editor can be used. Press A to select all keyframes and then G20 will move them forward twenty frames.
Another option is to use a script that sets the filename before rendering each frame, this answer should give you an idea how to do that.