everyone might lay claim to the same Guruparampara (earliest names)from
Narayana up to a certain point, so that part would be same for many traditions
until they lay claim to their own individual Parampara and distinct Guru lineage
you can learn the whole TM puja now and do it yourself. Nothing wrong with
that. Actually you can take Maharishi as your personal Guru now as explicitly
in the Vedic tradition once the Guru is no longer around to tell you no then
you can assume his answer is yes. Dont go and eat beef ever again if you do
this though!! The Guru will take it as a big offense.
A lot of the Vedas is exact same material repeated elsewhere or with a
different order or different style, if you do some basic research you can find
the particulars of that.