Can I give the baby her biological father's name?

In order to be listed on a child's birth certificate, most states require unmarried fathers to sign an affidavit or acknowledgment of paternity. It is a good idea for both parents to write, sign, and notarize a statement acknowledging the father's paternity. You can take this one step further by contacting your state's Vital Statistics office - which issues the birth certificate - and asking whether they keep paternity statements on file. If they do, make sure yours is filed. This also helps with establishing paternity for custody and support issues that may arise if you two do not remain together or marry after your divorce is final.  And it helps the child with inheritance issues should that come in to play.

Some states also allow and acknowledge an Affidavit of Non-Paternity which would be signed by your not-yet-divorced-from husband.  You should probably contact an attorney to make sure that everything is done correctly and all parties are protected.