From BiblePortal Wikipedia

Hastings' Dictionary of the New Testament [1]

(Ἀπελλῆς, a Greek name possibly contracted from Apollodorus , and apparently common among Jews of the Dispersion [cf. Hor. Sat . i. 5. 100: credat Iudaeus Apella , and Gow’s suggestion, ad loc. , that, as modern Jews take a Gentile name which closely resembles their Hebrew name, so in ancient times a Jew called Abel might choose the name Apelles]).-Apelles, saluted by St. Paul in  Romans 16:10, is called ‘the approved in Christ’ (τὸν δόκιμον ἐν Χριστῷ). The phrase may indicate that he had been specially tested and tried by affliction or persecution, or that he was a Christian who had gained the approbation of the Church, sufficiently perhaps to be called to the ministry (cf.  1 Timothy 3:10). Nothing is known of Apelles beyond this reference

Assuming the Roman destination of these salutations, he was probably a Jewish convert residing in Rome as a member of the Imperial household. As the salutation which follows is that to ‘the household of Aristobulus,’ it has been suggested that Apelles’ Christian activity may have lain in that direction. If Aristobulus ( q.v. [Note: quod vide, which see.] ) was the grandson of Herod, Apelles would no doubt find in his ‘household’ many members of his own race. The name Apelles is known to have belonged to the Imperial household. It was borne by a famous tragic actor in the time of the Emperor Caius (see Lightfoot, Philippians 4, 1878, p. 174).

T. B. Allworthy.

Hastings' Dictionary of the Bible [2]

APELLES . The name of a Christian who is greeted by St. Paul in   Romans 16:10 , and who is described as the ‘approved in Christ.’ It was the name borne by a distinguished tragic actor, and by members of the household.

Smith's Bible Dictionary [3]

Apel'les. (Called). A Christian saluted by St. Paul in  Romans 16:10. Tradition makes him bishop of Smyrna or Heraclea. (A.D. 55).

Fausset's Bible Dictionary [4]

A Christian saluted in  Romans 16:10 as "approved in Christ." A common Jewish name, probably not, as Origen thought, Apollos. Said to have been afterward bishop of Smyrna.

Morrish Bible Dictionary [5]

A Christian of Rome saluted by Paul as 'approved in Christ.' Rom. 16:10.

Holman Bible Dictionary [6]

 Romans 16:10

Easton's Bible Dictionary [7]

 Romans 16:10

International Standard Bible Encyclopedia [8]

a pel´ēz Ἀπελλῆς Apellḗs A C Romans 16:10 James 1:12 2 Timothy 2:15 Satires

Kitto's Popular Cyclopedia of Biblial Literature [9]

Apel´les, a Christian at Rome, whom Paul salutes in his Epistle to the Church there ( Romans 16:10), and calls 'approved in Christ,' i.e. an approved Christian. According to the old church traditions Apelles was one of the seventy disciples, and bishop either of Smyrna or Heracleia.