Hiding identifying data while allowing matching?
Any transformation of the identifier, including those in the question, is bound to have at least one drawback: after a transformation of cryptographic quality, it will be next to impossible to re-agregate identifiers that refer to the same person but have been slightly garbled (perhaps because there are two common spelling of the mother's name).

Even ignoring that, I do not see a convenient and bulletproof solution, basically because you start from a very short identifier.

One improvement would be to encrypt the identifier using a secret key, with format-preserving encryption, so that the encrypted result remains short, compatible with existing practice, and the encryption demonstrably can't introduce more collisions than there is originally. A most serious problem then is protecting the secret key, and limiting its use (which is necessary since it is enough to encipher a few chosen inputs to break the system).

Better than nothing is making this key passphrase-protected (like a PGP key is), with the passphrase entered on the laptop by the legitimate user at the beginning of data-collection activities. Standard key stretching techniques can make that quite safe against passphrase search, while still robustly detecting an accidental mis-keying. While we are at it, all data collected should be kept encrypted with standard techniques (using a different key, possibly protected by the same passphrase for convenience).

Even better is moving the key in a Smart Card, protected by user PIN with consecutive errors counter. Next step (recommendable, and quite easy even with standard Smart Cards) if moving at least a building block of the format-preserving encryption into the Smart Card itself, so that the key never leaves the Smart Card (said building block could be AES or a MAC, and the corresponding key, used in the round function of a Feistel cipher). Ultimately, the sensitive data could be held in the Smart Card itself and inaccessible without the PIN.

Beware however that nothing in the above can resit an active compromise of the laptop (e.g. key logger) performed before sensitive data is entered.