if a player plays 41 games for a team then is traded at the deadline?

You cannot get your name on the Cup, HOWEVER you can be voted a playoff share. In 1993-94 the Rangers traded Mike Gartner and Tony Amonte at the trade deadline, both players received a half share as part of the Stanley Cup money.

A player needs to be in the roster at the time of winning the cup to be considered for engraving

Here's the entire passage from Page 77 of the 2009-2010 Stanley Cup Rule Book

To have their name engraved on the Stanley Cup, a person must

a) be a player on the team's extended roster

and

1) have played a minimum of 50% of the team's regular season games

or

2) have played in at least 2 playoff games

or

3) have been petitioned by the team executive

or

b) be a member of the team's active management group

a3 is known as the Hartman rule because it was used by the Rangers at MIke Hartman's request (he was injured an unable to play 41 games or in the playoffs and he felt it unfair) to get both Hartman and Ed Olczyk's names on the cup. The petition is voted on by the Hall of Fame and not the NHL

I think it more goes by the teams choice then automatic. I will agree that by rule they played the 41 games so they would have it on, but I just think they are more likely to ask the team if the name should be on or not. I'd say LITY could give a more definite answer on how it works.

Following up on the petitioning...if I remember correctly didn't Detroit get Konstatinov's name engraved on it in 98? He was in that bad car accident after the 97 playoffs and hasn't been able to play since.

You have to be a member of the team to get your name on the cup - that's the first requirement

The answer would be no...

The player has to have been dressed for at least one game in playoffs!

At least that is the way it used to be.

The commissioner also has the leeway to decide on whether a player has the right to be on cup.

Yes, according to the last "fun fact" in the link below (from the nhl's website)

Nope

no. your name only gets on the cup if you played for them in the playoffs.