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What 涵 means in a Chinese namehán

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涵hán · B
tier B

包容;涵养。

To hold — water contained, and the patience that goes with it.

1 处原典 · 1 部典籍 · 全部可核

僭始既涵 The oldest sense: to contain

乱之初生,僭始既涵。

When disorder first arose, the first encroachments were already being tolerated.

诗经 · 巧言 · our translation
The old commentary glosses 涵 as "to contain". Not cultivation — capacity to hold. 毛传释「涵」为「容」——这是这个字最早的用法:不是「有修养」,是「装得下」。名字取的是这一层。
涵养包涵涵之涵容清涵
In a name

Capacity to hold, before cultivation.

「涵」先是装得下,才是修养。