This is my scenario:
Does SIP or RTP provide for a way for me to view the other participants (their name or number) on the call?
Yes, if your UAC and your conference provider supports RFC 4575: A Session Initiation Protocol (SIP) Event Package for Conference State
In that case you would be able to establish a subscription (SUBSCRIBE) with the conference
event package and (subject to appropriate permissions, authorizations, etc. at the discretion of the conference provider) you will get NOTIFYed about conference events. What events to notify is at the discretion of the conference provider (note the language in the RFC, no MUSTs, some SHOULDs and MAYs):
3.6. Notifier Generation of NOTIFY Requests
Notifications SHOULD be generated for the conference state when a new
participant joins (i.e., gets "connected" to) or a participant leaves
(i.e., gets "disconnected" from) the conference.
Subject to a local focus policy, additional changes in participants'
status, changes in their media types, and other optional information
MAY be reported by the focus.
Changes in sidebar rosters SHOULD be reported by the focus to their
participants and MAY be reported to others, subject to local policy.
Changes in conference identifiers and service URIs SHOULD be reported
by the focus to the conference package subscribers.
Changes in other conference state information MAY be reported by the
focus to the conference package subscribers.
You can probably expect it from IMS CONF service according to 3GPP TS 24.605 and 3GPP TS 24.147