St. Paul was considered the Apostle to the Gentiles though he never physically met or learned from Jesus, but through apparitions confirmed by St. Peter. Scripture also refers to St. Barnabas, Andronicus and Junia, Silus, Timothy, and Apollos as apostles.
The Catholic Church refers to the Vatican as the “Apsotolic See” and the college of bishops as the “Apostolic College”. The catechism says “The college of bishops, with whom the priests are united in the priesthood, makes the college of the Twelve an ever-present and ever-active reality until Christ’s return.” (CCC 1577) Furthermore, in general terms the “Apostolate” includes both ordained ministers and laity (CCC 864)–the whole body of believers are “called out” to share the Gospel and execise the gifts of the Holy Spirit.
The Church calls St. Mary Magdalene the “Apostle to the Apostles” since she told them about the resurrection. In the Eastern Church she is called “Equal to the Apostles”. Those called “Equal to the Apostles” were usually evangelistic pioneers who brought Christ to a new area. St. Mary Magdalene also has this title since she was a “proto-evangelist” after seeing the resurrected Jesus. St. Helena, Sts. Cyril & Methodios, St. Vladimir, St. Sava of Serbia, are just a few.
Similarly in the Roman Church we have many who are called “Apostle”: St. Frumentius (Apostle to the Abyssinians), San Juan de Avila (Apostle of Andalusia) Saint Gregory the Illuminator (Apostle to the Armenians), San José de Anchieta (Apostle to Brazil) St. Augustine of Canterbury (Apostle to the English), St. Peter Julian Eymard (Apostle of the Eucharist), St. Boniface (Apostle to the Germans), St. Patrick (Apostle to Ireland), St. Francois Piquet (Apostle to the Iroquois), Saint Faustina Kowalska (Apostle of Mercy), St. Columba (Apostle to the Scots), St. Adalbert (Apostle to the Polish)
I know the Mormons refer to their 12 elders as “Apostles” as do many Pentecostal-Holiness Protestants. In those cases they are doing so to somehow give their sect an air of legitimacy. Since Jesus gave the apostolic anointing to the 12, they are the ones who pass this on to subsequent generations. We call this “Apostolic Succession”. Thus, it is through union with the One, Holy, Catholic, and Apostolic Church that we become “apostles”. And it is for the Church to decide who legitimately can hold this title.