翻译成“律师身份号” 是可以的，不管它是律师证号码还是其他什么号码。

如果面向美加读者，把ID保留英文即可，比翻译出来要准确、清晰。

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Note added at 41 mins (2018-02-12 23:19:13 GMT)
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律师执业资格证号码

根据新泽西和明州律师协会的网页， 此两州的Attorney ID No 就是律师在该州考下执照时所颁发的执业证书上的号码， 就是律师通常挂在办公室里的那张纸上的号码。


NJ Attorney Index - NJCourts Online: Login - NJ Judiciary
https://portal.njcourts.gov/webe5/AttyPAWeb/pages/home.faces
This page permits the user to search for attorneys who have been admitted to practice in New Jersey, and to obtain information about attorneys, such as date of admission, status to practice law in New Jersey, and county and municipality of the business office of practicing attorneys. Use the attorney's Attorney ID Number to ...
Find an Attorney
www.padisciplinaryboard.org/for-the-public/find-attorney
Search by last name, first name, ID number, city, or county to look up an attorney. Search By ... The Disciplinary Board of the Supreme Court of Pennsylvania collects and maintains various information on all attorneys admitted to practice in the ... Some documents related to an attorney's prior discipline are accessible online.
Attorney Search
mars.courts.state.mn.us/
The following information is available on an Lawyer Search: License Number, Name, Address, Current Status, Admission Date, CLE Category,Professional Liability Insurance information. Where the Lawyer ID is unknown, a search for the Lawyer ID may be conducted by Last and First Name (both values required) or a ...

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Note added at 51 mins (2018-02-12 23:30:01 GMT)
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有的州叫做“律师执照号码”：

中国人如何获得纽约律师执照（NY state bar)? - 知乎
https://www.zhihu.com/question/20066510
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简单来说，通过NY BAR的考试+MPRE+Admission Application +宣誓即可获得执照。 从我自身经历来讲一下流程。我是加州某LLM毕业。 首先是LLM入学之后，尽早向考试委员会提交报名申请，NY BAR对于LLM报名的程序非常繁琐，需要你在国内的毕业证明、成绩单。之后如果有补充材料请补充材料。随后，LLM的第一学期 ...

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Note added at 59 mins (2018-02-12 23:37:18 GMT)
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律师执业资格（证）号码

律师执业证书号码，

律师执照号码

律师身份号码

律师ID号码

应该都可以。同一个东西在美国纽约和洛杉矶的叫法可能就有很大区别，没有统一的译文，完全取决于习惯叫法。题主的问题，我想只要不翻译成“律师身份证号码”，具体怎样措辞，可以很灵活。不能翻译成“律师身份证号码” 是因为那样翻译，无法与律师本人的身份证（例如驾照）上的号码相区分。