I would actually suggest you use your first and last name in the normal English speaking sense. I would suggest using the katakana version of your name when introducing yourself or else it becomes difficult to mentally process for them. Don’t worry about being exact.
Japanese generally know western names are first/last, but by giving both you allow them to respond respectfully to you. Most likely in the way of last name-san. If i’m reading it right, your last name is Lambert-Maberly? It’s most likely ease of use, but if you have a difficult last name, in this case they might choose to use first name-san.
If you see them struggling, you can also prepare beforehand.
アシュリーに呼びのは大丈夫です。
アシュリーはいいんです。