How true are the claims of this guy?
P.N. Oak is a controversial writer also known for claiming that the Vatican was once a Hindu temple.
Now onto the Taj Mahal, this claim is listed under Myths of the Taj Mahal
P.N.Oak's wikipedia states
In 2000 India's Supreme Court dismissed Oak's petition to declare that
a Hindu king had built the Taj Mahal and reprimanded him for bringing
the action, saying he had a "bee in his bonnet" about the Taj.
In fact you should read all of this entry.
Other than Oak's book itself, there do not seem to be other claims of the same.
So this seems to be a myth.
There are multiple theories about the name - and the offical website claims it actually stands for Crown Palace which is a literal translation of the words "Taj" and "Mahal"
There's more here
One of the legends is that the name Taj Mahal is derived from the
Persian language, the language spoken in Mughal court. In Persian, the
word Taj means Crown and the word Mahal means place or area. In
combination, the word Taj Mahal more or less means, "Crown Place" or
"Place of the Crown".