The Gerald (named after Gread Jones the manaer at Chester was a profitable service when it commenced with Class 57 + Mk 3 carriages and ran via Crewe which was conenient for passengers from North West England. The decision to divert the train via Wrexham was probably political and would have cost quite a lot of revenue.
Named after Gerald of Wales (Gerallt o Gymro), who documented Welsh life during his travels in the 1190s, on commission to Henry II and the Archbishop of Canterbury.
He's a curious mix of English and Welsh, being variously based in Pembrokeshire, Gloucester, Lincoln and Brecon.
I don't think there is a particular link to Chester.
The Gerald train began as an open access service over and above the ATW franchise spec, and funded directly by the WG.
In the 2018 franchise it became part of the wider TfW spec (with new/additional LHCS stock) so is now not directly subsidised.
It also now stops at Ludlow and Hereford so provides more "English" connections.
The initial route via Crewe was because there were no suitable paths via Wrexham.
While I too miss the link via Crewe, the hourly Manchester-Cardiff service does the north-west job, and Wrexham needed better than its previous 2-hourly service to Birmingham.