When a wallet is scanning for incoming transactions, every transaction is scanned to see if it is for "you". This only requires your private view key and your public spend key, and this check is immutable and cannot be faked. You cannot receive transactions and identify them without a corresponding private view key.
A transaction can be uniquely identified with the use of an optional Transaction ID, which is usually represented by a 32-byte string (64 hexadecimal characters).
