Here are some Halo Forerunner AI construct names, incorporating various stylistic approaches:

Formal & Hierarchical:

• Promethean-097-Xi
• Construct-Epsilon-Prime
• Archivist-743-Omega
• Guardian-Nexus-Alpha
• Sentinel-Prime-Custodian
• Monitor-001-Aether
• Oracle-Delta-Foresight
• Harbinger-Gamma-Revelation
• Enforcer-Zeta-Judgment
• Executor-Eta-Command

More Evocative & Mysterious:

• The Silent Watcher
• The Data Weaver
• The Logic Engine
• The Temporal Shepherd
• The Binary Heart
• The Obsidian Mind
• The Forerunner's Echo
• The Recursive Dream
• The Digital Ghost
• The Unseen Hand

Combines Formal & Evocative:

• Promethean-097-Silent Watcher
• Construct-Epsilon-Prime-Data Weaver
• Archivist-743-Omega-Logic Engine
• Guardian-Nexus-Alpha-Temporal Shepherd
• Sentinel-Prime-Custodian-Binary Heart

Short & Punchy:

• Aether
• Nexus
• Omega
• Harbinger
• Custodian
• Oracle
• Sentinel
• Executor
• Enforcer
• Archivist

These names aim to capture the essence of a Halo Forerunner AI construct, balancing the technological and potentially ominous aspects of their nature. Remember that you can combine elements from different categories to create even more unique names.