I have the name of a person who has since been married and moved to Quebec
How can I find out her married name and address for my small claims papers to serve her and do I use her married name even if the contract was in her maiden name?

If you know what jurisdiction the debtor was married in you may be able to check the local marriage records otherwise you may need to hire the services of a professional investigator.

We have heard, although we have not confirmed, that women are not permitted to take their husbands name in Quebec.

In Ontario, where we practice, you may sue someone using variations of their name. For example, Jane Doe also known as Jane Smith.

In case you are unaware, Quebec presents its own challenges with respect to litigation and you may wish to consult with someone in the province before commencing any action.

Cannot answer in Quebec but in most other jurisdictions a married woman is also known as (A/K/A) her previous married name. You would sue Jane Doe a/k/a Jane Smith.