You seem to be most concerned about your reservation, but on German trains it is the ticket you should be most concerned about. Without a valid ticket, you may be charged a fine (and potentially prosecuted — commonly repeat offenders only) and may be removed from the train. Without a valid reservation, you can just sit anywhere else. If you can make convincing phaenotypical arguments that you need a seat (i.e. you have a medical condition or are a fragile-looking senior citizen), somebody will vacate one for you upon request. Reservations are also not checked by the train staff but tickets are.
For most cities in Germany that have multiple long-distance train stations, these are treated as if they were the same station. So while your itinerary may read Berlin central to Leipzig, you can also get on the train in either Berlin Gesundbrunnen or Berlin Südkreuz at no extra cost. Typically, for these kind of stations tickets are not checked until the final one is reached and the train staff perform other general tasks and show availability for questions during that time.
However, unluckily the stations of Hamburg (central) and Hamburg-Harburg belong to two different clusters, treated differently by fare rules. This can be found in DB’s gigantic PDF file of stations treated equally.
But then again, this will likely not matter much. Since there is so little time (by IC(E) standards) between Hamburg central and Hamburg-Harburg, the train staff will likely not bother performing any checks until they left Harburg. You may possibly even get away with buying a ticket to Harburg but boarding/alighting the train in Hamburg central. (Note however, that I am not recommending it. If I do it, I get caught by Murphy’s law every time.)
Since your ticket reads Hamburg (not HH-Harburg), both boarding and alighting in Harburg can easily be done without any risk: The train staff have no means of finding out whether you boarded at Hamburg central, Altona or Harburg, and if you left the train before your ticket’s final station, that’s your problem.
As mentioned, the staff don’t care about your reservation unless you approach them with an issue. As other answers have already stated:
- reservations are typically displayed as city to city, not station to station
- you can claim your reserved seat up to 15 minutes post-departure before you forfeit it.
The second bullet points has a number of caveats, though. For one, many people don’t know about the 15-minute rule and will vacate your seat if you approach them showing your reservation. For two, the 15 minutes should count from Hamburg central, since that is the Hamburg-cluster’s mother station. Reason: All reservation displays from a certain city typically disappear at the same time.
As a final note, I want to restate that often people will sit in your seat. After you have confirmed being on the correct train and in the correct car, simply approach them and ask to get your seat, saying it is reserved. They were probably sitting there because they were feeling lucky or because they didn’t check the display. Regularly, reserved seats remain unclaimed.
: There is a journey distance cutoff for this which is usually 100 km. Taking an ICE from (e.g.) Augsburg to Munich will have different fares depending on whether you alight at Pasing or Munich central.
: You will need to click the Liste der gleichgestellten Tarifpunkte link below the linked FAQ entry to download the document — a direct link to the PDF seems to be very prone to linkrot. Help for reading the German document: The first column tells you what your ticket (or reservation) will say. The third contains a list of stations that are deemed equivalent with the ‘mother station’ (the one determining price and distance) bolded. The fourth column is the distance cutoff, i.e. you need to travel at least that far to benefit. If there is a star in the second column, the information is not valid for regional commuting tickets.
: This is true for every city that has multiple stops for long-distance trains: Hamburg, Berlin, Hannover (during fair times), Munich. Note the exception: Frankfurt airport is typically considered a separate station but only very few long-distance trains call at Frankfurt airport and the central station.