I am British, If I change my passport name, would other countries know my old name?

The chip in UK biometric passports only contains the info printed on the passport, including the picture (some other countries, in particular most EU countries, also have fingerprints but not the UK). I am not aware of any international norm or recommendation to include anything else. So if your passport contains no reference to your previous name (some comments and the passport application instructions suggest that, contrary to your assumption, UK passports would in fact generally include previous names), there is no reason for it to show up when reading the contents of the chip.

The main use for machine readable or biometric passports is to perform database lookups very easily, without having to type anything. In particular, your passport details can be checked against lists of stolen documents (e.g. from Interpol or the Schengen Information System) and your name can be matched against databases of outstanding warrants or lists of people banned from entering or can potentially be used to see your travel history in and out of a specific country (if the country in question maintains a database of entries and exits, which some do).

I don't precisely know what's possible in which country but I guess it should also be possible to search such databases using, say, the date and place of birth and, with a bit of time, to zero in on previous records under another name. So it could be possible to identify you if you somehow attract attention and are selected for secondary inspection, even if the passport does not mention your previous name. But this would not immediately show up upon scanning the passport.

Theoretically, the picture on the chip could also conceivably be fed to some facial recognition software and matched to previous records. But this is more difficult than movies make it look and I would be very surprised if any country was currently doing that routinely.

Importantly, governments obviously don't make detailed individual data about their citizens broadly available to all other countries in the world (think about the logistics and politics of something like that!). So it's just not possible for a random border guard in a random country to instantly get private info about you from the UK government beyond what's already on the passport and its chip. Of course, what's shared with the intelligence services of a few close allies like the US is anybody's guess but that's another matter entirely.

If you want to know precisely what information shows up when your passport is scanned...

You can take your passport to any public office of the UK Identity and Passport Service and use their scanner to see the information that appears.

This service is available to anyone who possesses a United Kingdom (GBR) Biometric Passport.

The information will not include alerts and open warrants because these are not maintained in the passport itself. Similarly, information about immigration history, deportations and removals are kept elsewhere. Also previous passports.

Having said that, your current name and previous names are pieces of text that do not have significant meaning in their own right. It is the linkage of passport number and previous passport number and any biometric data that count in recognizing you (or your 'friend') as a person of interest.

Adding...

To clarify the scope because of commentary: Note that when a UK border guard scans a UK passport, what they get back includes not only the chip info, but also an 'action code' which is returned from the Home Office database, but your question is about a foreign government scanning a UK passport. Different situations altogether.

Also, the notion that the chip itself implements multiple levels of access control may sound plausible, but it's without substance. It takes a standard passport chip reader.

If you have a friend with an Android phone with NFC capabilities, you can check some of its content yourself with this app (this app won't be on the iPhone, there is no third party NFC api access on the iPhone yet).

If they were to get their name of their British passport changed and visited countries outside the EU.

What do you mean by outside the EU? Were those other countries he wants to visit ever part of the Commonwealth? If so, there is a risk. If one of those countries is the US, I assume that he hasn't had his retina scanned yet, otherwise he wouldn't even be asking this question.

If he's going to South Korea, his name may not matter there. All he has to be is the right age and of Korean descent to be drafted for military service, even if he doesn't speak a word of Korean.

In the US, it's the credit reports that are very flexible and designed to show all the information that correlate with multiple identifiers (even if several identifiers do not match at all). US Border Control however, I really doubt that it has such a flexible system.

In any case, if your friend does change his name. He may just want to change his first name only. Even if a foreign government could find several matching identifiers through data mining alone, it would be difficult to know that he wasn't a twin (without asking him directly about it).

The premise of this question is leading, I fear to a mistake. a passport will carry enough information to uniquely identify its owner. That's for sure. The question you need to ask is, 'under what circumstances does the UK share detailed information about its citizens with other countries?' The passport itself isn't relevant. Chances are, if you get to country X, country's X's computer makes an query to the UK computer, provides a unique identification of you from your passport, and gets back, if nothing else, a list of alternative names. This is the most basic sort of information shared; it's used for politically exposed person tracking (anti-money-laundering, terrorism, etc.) Certainly, if a person ever earned herself a spot on the OFAC list or one of the European PEP lists, all her names will be there. Of, for that matter, if a person trashed a stadium or did anything else that made her conspicuous to law enforcement, same deal.

I had a first hand experience with this matter. Outside europe even if you are wanted by any country outside europe or wanted by interpol and you had your name changed in your passport they would have no access to your previous name. But european countries share information about their citizens betweens themselves. Whether present name, previous or interpol wanted list. Be careful guys