Do you have to be an “entertainer” to be a celebrity? It should boil down to if the general public is aware of your name.
It's more a matter of whether one's name functions as a trade or service mark. The public is aware of the name Charles Manson, but that does not function as a mark.
For example, Steven Spielberg is a director. "Steven Spielberg" is his personal name. However, if you go to see a "Steven Spielberg Movie" then, in that context, "Steven Spielberg" functions as an adjective to describe what kind of movie one is talking about. In other words, in that context, "Steven Spielberg" distinguishes those movies from others in the marketplace.
The public is aware of a lot of people's names, but that doesn't mean that persons who are well-known, for one reason or another, derive value from their name on goods or services as a means of distinguishing those goods or services from others in the relevant market - which are typically in artistic, literary, or performing arts sorts of fields.
WIPO Overview 3.0 puts it this way:
http://www.wipo.int/amc/en/domains/search/overview3.0/#item15
1.5 Can a complainant show UDRP-relevant rights in a personal name?
1.5.1 Personal names that have been registered as trademarks would provide standing for a complainant to file a UDRP case.
1.5.2 The UDRP does not explicitly provide standing for personal names which are not registered or otherwise protected as trademarks. In situations however where a personal name is being used as a trademark-like identifier in trade or commerce, the complainant may be able to establish unregistered or common law rights in that name for purposes of standing to file a UDRP case where the name in question is used in commerce as a distinctive identifier of the complainant’s goods or services.
Merely having a famous name (such as a businessperson or cultural leader who has not demonstrated use of their personal name in a trademark/source-identifying sense), or making broad unsupported assertions regarding the use of such name in trade or commerce, would not likely demonstrate unregistered or common law rights for purposes of standing to file a UDRP complaint.
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The list of relevant cases suggests that artists and entertainers do better than business people or politicians:
Julia Fiona Roberts v. Russell Boyd, WIPO Case No.
D2000-0210, <juliaroberts.com>, Transfer
Dr. Michael Crichton v. In Stealth Mode, WIPO Case No.
D2002-0874, <michael-crichton.com>, Transfer
Tom Cruise v. Network Operations Center / Alberta Hot Rods, WIPO Case No.
D2006-0560, <tomcruise.com>, Transfer
Fields for Senate v. Toddles Inc., WIPO Case No.
D2006-1510, <virginiafields.com>, et al., Denied
Jacques Chardeau, et al. v. MindViews,LLC, WIPO Case No.
D2008-0778, <caillebotte.com>, Denied
Margaret C. Whitman v. Domains For Sale, WIPO Case No.
D2008-1534, <megwhitmanforgovernor.com> et al., Denied
Jim Carrey v. BWI Domains, WIPO Case No.
D2009-0563, <jimcarrey.com>, Transfer
Jay Leno v. Garrison Hintz,WIPO Case No.
D2009-0569, <weeknightswithjayleno.com>, Transfer
Vanisha Mittal v.
[email protected], WIPO Case No.
D2010-0810, <vanishamittal.com>, Denied
Ananyashree Birla v. Ali Madencioglu, WIPO Case No.
D2013-1123, <ananyashreebirla.com>, Denied
Tracy Morgan v. Fundacion Private Whois / PPA Media Services, Ryan G Foo, WIPO Case No.
D2013-0078, <tracymorgan.com>, Transfer
Ananyashree Birla v. Ali Madencioglu, WIPO Case No.
D2013-1123, <ananyashreebirla.com>, Denied
Philippe Pierre Dauman v. Dinner Business, WIPO Case No.
D2013-1255, <philippepierredauman.com>, Denied
Adam Anschel v. Domains By Proxy, LLC / Tzvi Milshtein, WIPO Case No.
D2015-1570, <adamanschel.com> et al., Transfer
Victor Topa v. Whoisguard Protected / “Victor Topa”, WIPO Case No.
D2015-2209, <victortopa.com> and <victortopa.md>, Denied
David Michael Bautista, Jr. v. Quantec LLC / Whois Privacy Services Pty Ltd / Lisa Katz, Domain Protection LLC, WIPO Case No.
D2016-0397, <davebautista.com>, Transfer