Demons gain power through destruction of their enemies...
A demon's status grows with the blood it spills; the more enemies that fall before it, the greater it becomes. A demon might spawn as a manes, then become a dretch, and eventually transform into a vrock after untold time spent fighting and surviving in the Abyss.
The greatest of those that do survive make up the ranks of the demon lords that threaten to tear the Abyss apart with their endless warring. (DnD 5e Monster Manual, page 50)
This confirms that the entire "career" from a manes to a demon lord is indeed possible for a demon by simply destroying demons or other enemies in its way, and avoiding similar fate.
...or through demonic promotion
By expending considerable magical power, demon lords can raise lesser demons into greater forms... (DnD 5e Monster Manual, page 50)
This sort of promotion allows promotion to the highest demonic ranks too, but this is rare because demons detest competition:
Demon lords only rarely elevate demons to the highest ranks, fearful of inadvertently creating rivals to their own power. (DnD 5e Monster Manual, page 50)
What happens when a demon changes form
What actually happens to a demon upon promotion is not known, apart from that it changes form as it grows in power. Since the transformation is not detailed, it is reasonable to assume that the demon remains otherwise unaltered, with its memories and personality intact.