Do any names start with 谦？
Here's an alternative point of view.

谦恭 is an okay Chinese name, albeit &quot;uncommon.&quot;

If you check out this article on zhummzyking的博客 it talks about 谦 as a surname.
Under part two origins the article explains:

二.姓氏渊源：
第一个渊源：源于礼法，出自春秋时期君子之道，属于以儒家礼法为氏。
谦，是春秋时期儒家学派所提倡的礼法，提倡恭谦退让为尚，有心谦和面谦之分，儒家强调以君子之风，面对同等地位之人，应在内心上恭顺谨慎、文良逊让，以显尊敬，其在史籍《史记·乐书》中就有记载：“君子以谦退为礼。”当然，如若社会地位不对等者，儒家就不讲求什么“谦”了。
春秋后期，有一些人以君子自诩，遂改以礼法为姓氏，即称谦氏，后有不少人改回原姓氏，但仍有坚持为谦氏者，世代相传至今，其姓源繁复，不可一论。

Then it talks about a fairly well known monk by the name of:

谦开善.

The page also mentions a second origin but I won't paste that here.

谦 is not a common surname, but it is indeed a last name.


How about 恭 then?
This is where the China Biographical Database (CBDB) comes in handy.
A search for names with 恭 in them provides many names, alternative names and courtesy names.
Names like:

陳彥恭



程嗣恭



孫恭

Multiple people have the posthumous name:

文恭

including 王珪 and 王綯.
If you go through CBDB's name list the number of 恭's is immense.

恭 is a legit name.


You might see some complaints about your name, but Chinese names are diverse and varied and after all you have evidence to back you up.