Call him "John" - after
in this phrase (They are going to call him John - after John, his grandfather). what is meant by (after John,)?
Solution 1:
Your sentence uses 'after' as a preposition. Here 'after' means 'the boy was given the same name as his grandfather, which is John.'
See definition 11 of after (preposition) in Collins:
- PREPOSITION.
To be named after someone means to be given the same name as them.
[British].Phillimore Island is named after Sir Robert Phillimore.
He persuaded Virginia to name the baby after him.