Yes. In Jainism, a lay follower who has accepted the anuvratas is generally called a śrāvaka (male) or śrāvikā (female). More specifically, such a person is often described as a vratadhārī śrāvaka/śrāvikā or a deśavirata lay follower, meaning one who observes partial vows.

In simple terms:

• Śrāvaka / Śrāvikā = lay Jain follower
• Vratadhārī = one who has taken vows
• Deśavirata = one who observes partial restraint through anuvratas

So the special term is usually deśavirata śrāvaka/śrāvikā.