I started a process to use my dads name for a community blood drive. My youngest sister his blood child says I no rights and if I keep presuing this issue she will charge me with unlawful use of his name. I only know him as my dad even though I am only a step child. Growing up we never used the term step child or dad.

Legally, your name is what it is on the birth certificate. If you are an adult you may go to court and see about having it changed. ( merely a name change, it does not give you any status as his daughter)

If you are a minor child, step dad can see if your bio dad will sign over his rights and allow him to adopt you.

For non legal things, you can call yourself, wolfdog if you want, since it is not illegal, merely not using your real name.

... if I keep presuing this issue she will charge me with unlawful use of his name. ...

She doesn't have a leg to stand on. The name isn't copyrighted. If you aren't defrauding anyone, go for it.

I started a process to use my dads name for a community blood drive. My youngest sister his blood child says I no rights and if I keep presuing this issue she will charge me with unlawful use of his name. I only know him as my dad even though I am only a step child. Growing up we never used the term step child or dad.

It is not unlawful in any manner. In fact, I'd be honored to have someone use my name in a blood drive.

Tell your stepsister good luck; if she actually tries suing you, the judge will laugh her out of court.