Anabia is not an Arabic/Quranic word, on many Pakistani websites this name is wrongly mentioned as a Quranic word. The correct Quranic word is Anaba, and it means "he/she made repentance and returned to Allah" as you wrote. None of the doors of Paradise have a name like this.
Anaba can be used as a name, though it is more common to use its noun version of Muneeb for boys and Muneebah for girls (meaning someone who repents and returns to Allah). In Quran 11:75 Allah SWT describes prophet Ibrahim with this name.
Indeed Ibrahim is most forebearing, most tender-hearted, and intent upon turning to God again and again.