Theft of identity is often a route to stealing money in your name, although it can also result in someone else living elsewhere but using your identity.
The identity thief may start by scanning through blogs and facebook pages looking for someone who is likely to have the right credit rating, and reveals enough about their real life, family and work to make the theft possible. Or they may start by looking for documents thrown out in your rubbish that have correspondence from bank, tax, medical or other official correspondence.
With this detailed knowledge of your life they may attempt to get your address changed, so that official correspondence goes to an address the criminal controls, and as soon as that happens they can use that as supporting evidence to take out a loan or mortgage using your details, or to get a new passport issued or other official documents. As soon as they have the money and or documents they move on, perhaps selling the passport for someone else to use, with your name on it to live in a different country.
Many organisations will send a letter to your old address detailing the change of address whenever they are asked to change your old address. Don't ignore a change of address notification if you didn't request it.
The identity thief may also use a stolen mobile phone or attempt to take over your mobile phone number and use that as a route to stealing your email account. If they only have to switch on your mobile phone to use your email address, then they can reset your passwords or can use your banking apps to transfer money from your account to theirs. With full access to your accounts it is much easier for the thief to obtain documents in your name.
Make sure that your mobile needs a password or fingerprint to log in.
Use a free service to check your credit rating at regular intervals. There are also reputable services that will email you an alert whenever there is any change to your credit rating.