Actually, it turns out the repeater does not have to ID itself (though it's a good idea anyway) as long as the repeated station does ID itself.
Sec. 95.119 Station identification.
(a) Except as provided in paragraph (e), every GMRS station must
transmit a station identification:
(1) Following the transmission of communications or a series of
communications; and
(2) Every 15 minutes during a long transmission.
(b) The station identification is the call sign assigned to the GMRS
station or system.
(c) A unit number may be included after the call sign in the
identification.
(d) The station identification must be transmitted in:
(1) Voice in the English language; or
(2) International Morse code telegraphy.
(e) A station need not identify its transmissions if it
automatically retransmits communications from another station which are
properly identified.
[48 FR 35237, Aug. 3, 1983, as amended at 63 FR 68975, Dec. 14, 1998]
Sec. 95.33 Cooperative use of radio stations in the GMRS.
(a) Licensees (a licensee is the entity to which the license is
issued) of radio stations in the GMRS may share the use of their
stations with other entities eligible in the GMRS, subject to the
following conditions and limitations.
(1) The station to be shared must be individually owned by the
licensee, jointly owned by the participants and the licensee, leased
individually by the licensee, or leased jointly by the participants and
the licensee.
(2) The licensee must maintain access to and control over all
stations authorized under its license.
(3) A station may be shared only:
(i) Without charge;
(ii) On a non-profit basis, with contributions to capital and
operating expenses including the cost of mobile stations and paging
receivers prorated equitably among all participants; or
(iii) On a reciprocal basis, i.e., use of one licensee's stations
for the use of another licensee's stations without charge for either
capital or operating expenses.
(4) All sharing arrangements must be conducted in accordance with a
written agreement to be kept as part of the station records.
(b) [Reserved]
[48 FR 35237, Aug. 3, 1983, as amended at 63 FR 68975, Dec. 14, 1998]
The FCC doesn't pay much attention to the written records part, true... but it is in the regulations.