抜ける and 抜く: missing parts and taking things out
Compare a tooth coming out with unplugging something, and examine omissions and skipping meals with standalone 抜く.
Something comes out of its place
子どもの乳歯が抜けました。 says that a child's baby tooth came out. 抜ける, read ぬける, has the removed item as subject and does not identify anyone pulling it out.
プラグをコンセントから抜いてください。 asks someone to unplug the plug from the outlet. With 抜く, read ぬく, を marks the item and から where it is removed from.
A missing item in a document
名簿から私の名前が抜けています。 says that the speaker's name is missing from the list. It describes an omission, not a physical name tag falling out.
重複した行を抜いて、表を短くしました。 says that someone removed duplicate rows and shortened the table. 抜く also describes excluding a part of some content.
Skipping a meal and verb forms
時間がなくて、朝食を抜きました。 says that someone skipped breakfast because there was no time. 朝食を抜く means not having the meal, not physically extracting it.
抜く becomes 抜いて, and 抜ける becomes 抜けて. 空気が抜けた reports air escaping, whereas 空気を抜いた describes someone letting it out.
What state of the name does 名簿から名前が抜けています describe?
Show the answer and why
It means that the name is missing from the list. It does not identify anyone deliberately deleting it.