🔼The name Shelah
There are two completely different Hebrew names in the Bible that are commonly both translated with Shelah. But they're spelled different and they mean different things. We'll call them Shelah I (שלח) and Shelah II (שלה):
🔼The name Shelah I in the Bible
The only Shelah I (שלח, more properly pronounced as Shelach) of the Bible is a son of Arpachshad, son of Shem, son of Noah (Genesis 10:24). This Shelah was an ancestor of Christ, and is mentioned by Luke (spelled Σαλα, Sala; Luke 3:35).
🔼Etymology of the name Shelah I
The name Shelah-with-heth comes from the root group שלח (shalah I and II):
Abarim Publications' Theological DictionaryLoading: שלח (or click this link)
🔼Shelah I meaning
Assuming that Shelah wasn't named after a table, the name Shelah (שלח) may mean Sent Out, Branch or Javelin. For a meaning of the name Shelah (of either spelling) NOBSE Study Bible Name List appears to go with Shelah I and reads Sprout, Request.
🔼The name Shelah II in the Bible
There are two characters in the Bible that are named שלה, namely:
🔼Etymology of the name Shelah II
The name (שלה) Shelah-with-he seems to be related to the root group שלה (shala I & II):
Abarim Publications' Theological DictionaryLoading: שלה (or click this link)
The name Shelah (שלה) means all of the above, but would probably be interpreted to mean either Prosperity or Booty.
Jones' Dictionary of Old Testament Proper Names disagrees with all these obvious similarities, and takes the name Shelah to be a syncopated (= shortened by omitting the letter in the middle) form of the noun שאלה (she'ela), meaning to request or demand:
Abarim Publications' Theological DictionaryLoading: שאל (or click this link)
This would relate the name Shelah to the name Saul, and thus Jones translates this form of the name Shelah with Prayer.
From a linguistic point of view this may or may not be correct, and Prayer may be the original meaning of the name Shelah, but to a Hebrew audience, especially the non-linguists, the name Shelah looks like it means Prosperity.