Hello, name is used as a verb, and it usually has 5 uses:
1) Name...; name..., such as the two sentences you mentioned:
Tom named his pet kitten Happy.
（Tom named his pet kitten Happy.）
Peter named his model Theme Park.
（Peter named his model Paradise.）
She decided to name the child Edward.
（She decided to name the child Edward.）
2) Confirm the name of…; give the correct name of….
The dead man has been named as John Mackintosh.
(It was identified that the deceased was named John Mackintosh.)
3) Use some kind of title (or nickname) to address; to confer on... a certain title. For example, you mentioned that Peter named his model Paradise.
Peter was named as Student of the Year.
（Peter was named the best student of the year.）
4) Mention; quote.
This park was named in the novel.
（This park was mentioned in the novel.）
5) Decide; decide (amount, time or place)
The club has asked Tom to name their price for the goalkeeper.
The club has asked Tom to name their price for the goalkeeper.
The club has asked Tom to name their price for the goalkeeper.