Why did New Labour re-brand Social Welfare Payments as Tax Credits?

Marketing.
The last 40 years of government has been nothing else.

Its like the Labour Exchange becoming the Job Centre. (70's/80's)
Or Polytechnics becoming Universities. (80's)
Next it's Universal Credit (2013 act)

Bedroom Tax becomes.... Removal of the Spare Room Subsidy(social sector).

Is this the party who was led by Tony Blair the Middle East Peace Envoy

It's the sort of thing that appeals to leftists and labour voters , they're dishonest in that way .

Tax credits is a low income subsidy or also know as a subsidy for employers who don't pay their employees enough to live on/give them enough hours.

The other problem is that tax credits were designed by people who had only known constant, permanent, salaried employment, and who imagined everyone else was the same.

This meant low-paid people whose income varied from one week to the next could find themselves in trouble for over-claiming or hungry through under-payments.

You can blame labour for that also, that`s what you voted for. free movement of labour

The Tax credit system actually encourages minimum wage earners not to work more than 30 hours a week.