Many people are born in non‑Jain families but try to follow Jain principles in their life. In general, such people are simply called:

• “Jain dharm se prerit” (inspired by Jain dharma)
• “Jain tatvo ko maanane wale” (those who accept Jain principles)
• In English, often: “Jain‑oriented”, “Jain‑principled”, or “followers of Jain philosophy”

There is no special fixed technical term in Jain scriptures only for “non‑Jain by birth but following Jainism.” In practice:

• If someone takes formal vows (anuvrat, shravak pratima etc.) from an Acharya / Sadhu, they may be counted as Jain shravak/shravika, even if not born Jain.
• If they just admire and practice a few principles (ahimsa, vegetarianism, aparigraha), they are usually described only as “inspired by Jainism,” not formally Jain.

So the name/term is mainly:

• Jain dharm se prerit vyakti
• Jain tatvopasak (one who worships/follows Jain principles)

Different societies or groups may use their own words, but in Jain dharma literature this is the simple way to describe them.