Name : Aubin
Place : Unknown
Query : What does it mean to have sun and moon conjuct in 10th house?

Aubin,
According to Vedic astrology my comments are as follows:
Sun is digbali in tenth house (directional force is best), conjunct Moon, is indicating – Person will enjoy authority, power, but may face some issues/trouble. If auspicious aspect then soft ruler, if malefic aspect then cruel ruler, but under both conditions judicious ruler.
According to Classics – love discipline, and enjoys status of a ruler, or holds key position.
This is in general condition.
This may change according to the lordships and other aspects or conjunctions etc.
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