Did medieval king ships resemble Ark Royal's renaming?

Is calling vessels king ships or ships of the Tower comparable to Ark Raleigh becoming Ark Royal?

Broadly yes. The ship began as Ark Raleigh, built by Sir Walter Raleigh.

The comparison receives a brief agreement. Ark Royal began as Ark Raleigh, built by Sir Walter Raleigh. The example links a familiar ship name to the preceding discussion of vessels entering royal service. No further account of its acquisition is given here.