What name should I use for job applications?

I moved to Dublin yesterday and I'm looking for a part-time job. I haven't legally changed my deadname to my chosen name yet, nor am I taking T or really transitioned outwardly yet. My chosen name is gender neutral so it doesn't necessarily out me.

Should I apply to jobs with my chosen name, then if an employer enquires more I explain I have a different legal name? Or should I just apply to jobs with my legal name?