Lelouch's supposed to be dead and it'd be a safe guess to think that the Ashfords would have helped spread the word around, as payback for his late mother's support and protection.
Besides, it might have been a few months/years before the new government would have its databases up and running, so his decision to use his mother's maiden name might not have been done right after the invasion. By then, not only would the Emperor have deemed his two (disowned and useless after the invasion) children wasted and of no longer use and put an end to the search. Since he couldn't be used as a political tool anymore - or so it seemed - there was no reason to mobilize soldiers to look for them. As such, Lelouch could have easily adopted 'Lamperouge' right then and the name would have eluded the search efforts, as people are now busy with other things - like spoiling the shreds of a conquered land.
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Besides, it might have been a few months/years before the new government would have its databases up and running, so his decision to use his mother's maiden name might not have been done right after the invasion. By then, not only would the Emperor have deemed his two (disowned and useless after the invasion) children wasted and of no longer use and put an end to the search. Since he couldn't be used as a political tool anymore - or so it seemed - there was no reason to mobilize soldiers to look for them. As such, Lelouch could have easily adopted 'Lamperouge' right then and the name would have eluded the search efforts, as people are now busy with other things - like spoiling the shreds of a conquered land.