Puddle outside house when it rains

No, if anything you need more gravel. Or a properly constructed rainwater garden.

Any chance of a photo or two of the layout?

Drainage is what is needed, this could even happen within the gravel, as long as there is a drain or a lower-lying area for it to run into.

A few might be better, just need to see the layout and if there are options.

Is that a drive-way extension (ie, added in afterwards) over to the right of the photos? And that AJ/drain in the photo, is that rainwater or sewerage (I'm guessing it's rainwater)? If it is rainwater then have a drain installed there 90cms to the right of the AJ and make all your problems go away. No?

Access Junction - ie drain.

Time to lift it and have a look!

No, not really. You'd need a gully with a trap, or a linear/channel drain added into that concrete.

https://tjomahony.ie/building-materials/underground-pipe-conduit.html

So effectively like this with the orange pipe under the existing concrete:

Anyway, all very correctable as long as that AJ is for rainwater.

That's the catch. A good handyman would do it or a small-job builder, it's about a half-day's job to cut the concrete and then route the pipe under the existing concrete into the AJ, then fit the gully and backfill the hole with concrete and finish it off. It's a full-day of a job if more of the concrete has to be lifted. Check with neighbours to see if they have a reliable contact.

Decide whether you want a gully or a channel drain (all visible on that link I posted earlier).