I'm new here and I'm not sure if I'm supposed to use my maiden name or my married name.
Thank your for your post.
We recommend entering a women's maiden name, whether it is yours or another female ancestor. This helps the system look for records for them with that name. By entering a spouse, it will also look for her with her married name. You can also add her married name, a nickname, a legal name change, etc,. in the Other Information section of her detail page. Below is a link from the Help Center article about this.
Below are a couple more Help Center articles that might help.
Hopefully these articles will have answered your questions!
The name displayed when you make a contribution on Family Tree needn't have anything to do with any of your real names. My cousin's son uses a mashup of a Latin phrase, and many people use various combinations of initials and numbers. (I use my married name, because it seems to help keep my spouse's Famous Relative from getting too many spurious edits from wannabe relatives.)
What you enter for yourself on your FS account and on Family Tree is totally up to you; nobody will see it, just like nobody will see what you enter about living people. (I only use maiden names on the tree, including for myself.)