Why sometimes long vowels are not written?

Question

For example, David can be written in this way: דוד and this: דויד

So if you walk in My ways, to keep My statutes and My commandments, as your father David (דויד) walked, then I will lengthen[c] your days (1 Kings 3:14)

Then Samuel took the horn of oil and anointed him in the midst of his brothers; and the Spirit of the Lord came upon David (דוד) from that day forward. So Samuel arose and went to Ramah (1 Samuel 16:13)

Answer 1

An astute observer will note numerous names, both place names and personal names whose spelling varies in both the OT and NT. This not unexpected for several reasons:

• standardized spelling only arose in the 16th & 17th century AD
• different accents meant that people pronounced name differently and this is reflected in the different spellings
• some people used the older more complete form of a name and other used a simplified shorter form of the name (compare Silas vs Silvanus in the NT)
• in the case of the name "David", the two Hebrew spellings amount to "dawid" vs "dawiyd". Now, good cases can be made for the meaning of the name to be either derived from the word for "beloved" or "chieftain". Both are probably correct because when said in ordinary speech, both sound almost identical.

Thus, it is not surprising that spelling of names, including "David", varied.

Answer 2

Traditional Hebrew scholars gave importance to the appearance of every letter as imparting a lesson to the meaning of the text, not simply an inconsistency of spelling born of the times.

כתיב מלא - ktiv male - using vowel-letters vs כתיב חסר - ktiv chaser - omitting vowel letters

This article by Harel Shapira has a section speaking specifically about the letter yud י (the letter you noted was added in David's name in the book of Kings). He explains (based on the Zohar) that an additional yud is either symbolizing holiness or symbolizing a future event. He brings three examples supporting each option.