It think it could be *elen + sar or *eled + sar (or maybe something more specific has come to light recently).
In 1958 Tolkien wrote:
'EL. It is dificult to distinguish 'star' and 'elf', since they are derivatives of the same basic element EL 'star'; as the first element in compounds el- may mean (or at least symbolize) either (...) The Elves were called eledá/elená 'an elf' (High-elven Elda)...' JRRT, letter to Rhona Beare
A bit later in
Quendi And Eldar (fairly certainly dated 1959-60)
Note 10
'It is not surprising that the Edain, when they learned Sindarin, and to a certain extent Quenya also, found it difficult to discern whether words and names containing the element el referred to the stars or to the Elves. This is seen in the name Elendil, which became a favorite name among the Edain, but was meant to bear the sense of 'Elf-friend'. Properly in Quenya it meant 'a lover or student of the stars', and was applied to those devoted to astronimical lore. 'Elf-friend' would have been more correctly represented by Quen(den)dil or Eldandil.' JRRT Q&E
In this same text it's noted under *DEL:
'Eldo cannot however be directly descended from *edeló. Its form is probably due to a change *edelo > eledo, following the change in the verb.' Anyway Tolkien seems to have changed his mind later about
Elendil, as he wrote in a footnote to a letter...
'This provides the key to a large number of other Elvish Q. names, such as Elendil 'Elf-friend' (eled + ndil), Valandil, Mardil the Good Steward...' JRRT August 1967
Tolkien was not against changing his mind in any case