Where this number comes from: LinkedIn recommends 1584 × 396 for personal profile banners. Company page covers are a different size, 1512 × 256.
A profile banner is a 4:1 strip, which is an extreme shape: four times as wide as it is tall. Almost nothing photographed normally survives the crop, so banners that work are usually built for the ratio — a wide texture, a horizon, a graphic with space around it — rather than cropped down from a portrait.
Your profile photo sits over the lower left of the banner, and on narrow screens LinkedIn crops the strip inwards from both sides. Both of those eat into the same region, so anything that must stay visible belongs in the upper middle, away from the left corner and away from the outer edges.
Personal profiles and company pages do not share a size. A company cover is 1512 × 256, which is wider still at roughly 5.9:1, so a banner made for one looks wrong on the other.
Questions
Is this the same as a company page cover?
No. A personal profile banner is 1584 × 396. A company page cover is 1512 × 256. Using one for the other gets cropped badly.
Why is my banner cut off on mobile?
LinkedIn crops the strip inwards on narrow screens, so the left and right ends are the first thing to disappear. Keep text near the middle.
What file size is allowed?
LinkedIn accepts PNG and JPEG up to 8 MB for profile banners. At 1584 × 396 you will not get close unless you export PNG at full quality.