Multiple horns or no horns are technically allowed.
Tieflings in D&D 5e are described as having an unspecified number of horns, and while it is generally implied to be two horns and depicted so in art, this isn't strictly defined. It's also a valid variant to have no horns.
Multiple horns, but usually two
Player's Handbook p.42 notes:
Their hair, cascading down from behind their horns [...]
This implies that a tiefling's horns are located at the front of their head, and that a tiefling has multiple horns, most likely two. However, it doesn't strictly say "two horns", "a pair of horns", or the like, only that they have:
large horns that take a variety of shapes
It is therefore valid, by the wording of the rules, for a tiefling to have more than two horns. However, the rules do not appear to leave an opening for one-horned tieflings.
In older editions of the game, Asmodeus himself is usually depicted as having exactly two horns. This implies that tieflings should probably have two horns.
However, some tieflings have no horns. Sword Coast Adventurer's Guide p. 118, under the Tiefling Variants sidebar notes:
Since not all tieflings are of the blood of Asmodeus, some have traits that differ from those in the Player's Handbook. [...]
Appearance. Your tieflings might not look like other tieflings. Rather than having the physical characteristics described in the Player's Handbook, choose 1d4 + 1 of the following features: small horns; fangs or sharp teeth; a forked tongue; catlike eyes; six fingers on each hand; goat-like legs; cloven hoofs; a forked tail; leathery or scaly skin; red or dark blue skin; cast no shadow or reflection; exude a smell of brimstone.
It is therefore possible for a tiefling to have no horns, provided they are not of the blood of Asmodeus.
You can, of course, ask your DM if you wish to play something non-standard. This kind of minor detail of physical appearance does not affect game balance.