Name change on the plastic card

[GCer Chennai]

I would like to know how important the name on your plastic card is.

I talked to a couple of permanent residents whose names on the
plastic cards are different from the name they are known by;
and they said they never had any problems (their drivers license
has a different name than their plastic card).

My wife received her plastic card, and the name on her card is a little
different from her original name.

Instead of Last(A) Middle(BC) Fist(D) (middle name consisting of 2 words),
the name on her plastic card is Last(AB) First (Cd.).
d being the initial letter of her First name.

I am not sure if I should apply for a name change in this case.

Thanks for any info.
NameSeeker.