Short answer
Follow the physical vessel through builder, yard number, launch identity, ownership transfers, renamings, and major conversions. Names change more easily than hull identity.
Build a continuous identity chain
Builder / yard number
Usually the strongest starting point for proving continuity between names.
Launch name
The name under which the hull entered the water may differ from the name under which it became famous.
Transfer dates
Ownership, nationality, requisition, seizure, or sale can mark a new documentary phase.
Renaming events
A renamed ship may also receive new livery, interiors, machinery, or service classification.
Why this matters
Search results and secondary sources are often organized by ship name rather than hull identity. That can split one career across several records, or cause information from different phases to be combined incorrectly.
Physical continuity can coexist with historical discontinuity
A vessel may remain the same hull while becoming a very different historical object. Vaterland and Leviathan, for example, belong to one physical ship but to sharply different national, political, and commercial contexts.
Best practice: preserve both truths—one hull, multiple identities.