The WA court has the power to allow a minor to change the minor's names if the court believes changing the names is in the best interest of the minor, regardless of the consent of the legal parents.
If the facts presented in your post are true and proven, your daughter stands a good chance of changing her name.
Because she is 14, the court will ask her opinions as to whether and why her name should be changed.
That she has informally used the name she wants, the biological father's name is not on the birth certificate, and the father has not seen her in years are likely factors in favor of allowing her to change her name.
You appear to be still married. If your husband is willing to adopt your daughter and your daughter wants to be adopted, you may want to check into adoption. There are benefits in legalizing the relationship between the daughter and your husband if they want a relationship.
A petition to change name is relatively simple in WA: file a petition with the district court where the person lives, show up for a hearing (which can be on the same day as filing), the court asks a few questions to see whether the name change should be allowed. If the court finds the name should be changed, the court signs an order that the court's staff will file with the county's recorder's office. The fees to do the name change by yourself is about $150.
You should review your specific facts with local attorney to find out your legal options.