Under MA elder law, is it possible to name the person or persons I would want to have as my guardian if I should need one when I get older?
Yes it is possible, and many people do it. Under Massachusetts General Laws Chapter 201B, Section 3(b), a person can use their durable power of attorney to nominate the person they would be most comfortable with if they ever needed a guardian. Note that a person does not need to be an elder to make this decision.
Under this Section 3(b), if you nominate a person to act as your guardian, and proceedings to appoint a guardian for you are ever commenced, "The court shall make its appointment in accordance with the most recent such nomination by the principal except for good cause or disqualification." This is another reason why a well thought out estate plan, including a power of attorney, is so important. However, see this post for information about changes in the law regarding guardians and conservators.
UPDATE:
Under the new Massachusetts Uniform Probate Code, a principal may still use a durable power of attorney to nominate a person she would like the court to appoint as her guardian or conservator if/when such an appointment becomes necessary. See Massachusetts General Laws Chapter 190B, Section 5-503