The new small cylinder is centered within its larger predecessor. For aesthetics, and to make sure we have more space for our custom text, we'll want to move that new cylinder along the X axis and place it closer to the edge of our piece. For the most part, you can go with what looks good to the eye. The only stipulation is you will want to make sure you meet the minimum wall thickness of your printing process.
For Service Bureau Printing, I would consider leaving at least 1mm. For at-home printing, I would be more comfortable with 2mm:
You will want to keep minimum wall thickness in mind when positioning the new cylinder