Yes, the AM must air a legal ID hourly and the translators should follow the rules below.
Identification of translator and booster stations. Translator stations must be identified by the licensee by the following means:

... by arranging with the primary station whose signal is being rebroadcast to identify the translator by call sign and location. The identification must occur 3 times daily: once between 7 AM and 9 AM, once between 12:55 PM and 1:05 PM, and once between 4 PM and 6 PM. See 47 CFR Section 74.1283(c)(1)....

by transmitting the call sign in Morse Code at least once hour. See 47 CFR Section 74.1283(c)(2) for additional requirements for transmission of the call sign in this manner.