NO2ID

If a person was deported from a foreign country for say, tax evasion, and subsequently banned from re-entering that country for 5 years, would it be possible just to change one's name, apply for a new passport with the new name and be able to enter that foreign country again?

Would the new passport with the new name contain information indicating the recent name change and/or the previous name?

Almost certainly breaking someone's law.

But you have mistaken the purpose of this forum, which is to deal with changes in the UK passport/visa regime related to the National ID Scheme. Such questions would be off topic even if we could answer them.