Correction: it will not usually change the ticket number, nor do I think it will in the case described. Cases where the ticket number will change would include a different marketing carrier (i.e., switching to a UA flight from a non-UA flight), adding or removing a transfer, changing the date of a flight (e.g., SDC to the day before), or needing to pay a fare difference. There may be others, but simply changing from one UA-operated nonstop to another on the same day, in the same fare class, shouldn’t be one of them.