Seems to me, this would be Company A vs. Company B, unless this is about a temporary employment agency, in which case I believe the wording would be entirely different.

two subsidiaries within the same larger company, dude...

I can't imagine they'd call them "hirer" and :supplier." Of course, this is way above my pay grade, but maybe (since no one else seems to be answering) simply "subsidiary A" vs. "subsidiary B"?

Google: employee leasing agreement

An Employee Lease Agreement is an agreement between a lending company/employer (the Company) and another company (the Client) whereby the client agrees to contract for the services of the employer’s employee(s) according to specific terms and conditions. (...)the Company remains responsible for the payment of salaries and wages of the leased employees and is paid by the Client a set fee as set forth in Schedule B.
http://premium.docstoc.com/docs/21201337/Empl...

EMPLOYEE LEASING AGREEMENT
This EMPLOYEE LEASING AGREEMENT (“Agreement”) is made as of the 20th day of November, 2008 and effective as of the Closing Date subject to consummation of the Closing, between ..., LLC, a limited liability company organized under the laws of Delaware (“...”), and ..., a Canadian federally incorporated trust company (“...”). (...) 1. Leasing of Employees. ... agrees to lease to ..., and ...agrees to accept the services of, each Employee listed on Schedule 1 (the “Leased Employees”), for the period commencing as of the Closing Date and ending on March 31, 2009
http://www.sec.gov/Archives/edgar/data/133281...

oder einfach den Entleiher so benennen wie oben: "Client"

Arbeitnehmerüberlassungsvertrag = employee leasing agreement
überlassener Arbeitnehmer = leased employee
Ein beispielhaftes Muster von vielen (AE) siehe oben.

Wenn man im Rechtsenglischen von employee leasing sprechen kann, dann kann man die Vertragsparteien m.E. auch abstrahierend als lessor und lessee bezeichnen, wie bei anderen Leasingverträgen auch.

Juristendeutsch vs. English legalese.

edit löscht

"lending" an employee to another department is called a secondment. It is expected that the employee will return to his original work/department, after the secondment period is completed.

http://www.tbs-sct.gc.ca/faq/seas-eng.asp

I think for the Verleiher/Entleiher you would probably just keep the regular title of the department manager....but not sure

Manager X allows employee Y to be seconded/assigned to Manager Z ....

Dictionary: Arbeitnehmerüberlassung
= supply of temporary workers

Arbeitnehmerüberlassung = supply of temporary workers
http://iate.europa.eu/iatediff/SearchByQuery.do
(quasi-offizielle EU-Übersetzungsdatenbank)

Im konkreten Kontext aus dem OP würde ich die beiden Vertragsparteien Verleiher und Entleiher am Ende wohl so benennen.

# 7 hat zwar im Prinzip Recht, aber ich glaube nicht, dass es hier im OP um eine unternehmensinterne vorübergehende Versetzung handelt, sondern um das, was im Deutschen "Arbeitnehmerüberlassung" heißt, und das findet zwischen verschiedenen Unternehmen statt. (Supplying temp workers...)

Danke schön!!! :-)