This is the only case in which changing the name of a hockey related trophy makes sense. The Pearson lacks the both the historical significance of most of the NHL awarded trophies, as it is preceeded by many of them by over 40 years. It is also a somewhat redundant trophy, as most people take the Hart trophy to signify the same accomplishment.
The naming of the trophy is also somewhat mystifying. Pearson is arguably Canada's greatest Prime Minister but he had very little to do with hockey, not to mention having no relevance to any non Canadian NHL fans. Lindsay on the other hand was the most significant player in the formation of the NHLPA, the people giving out the award, in addition to being a great player. All other individual NHL related trophies of significance, with the exclusion of the plus minus trophy, are named after either someone very influential in hockey history or the person who in fact donated the original trophy. The justification for naming the award after Pearson is much weaker. As such, if there is any trophy that is fitting to have its name changed, this would be the one.
As far as this name change opening the door for further trophy name changes, ultimately the NHL always had the ability to change the names. This trophy is awarded by the NHLPA, a separate entity from the NHL. There is little evidence that what one does with their trophy will affect the other; if that was the case, the Pearson may have instead been called the Eddie Shore award, or the Mark Messier Leadership award may have been named for Pierre Trudeau instead.