There are lots of Hl names. Probably far more than you realized.

So I put together a little list of the names, trying hard to separate out by national origin.

Czech

Hlasny, Hlinka, Hlavacek, Hlavaty,
Hlubic, Hlavsa, Hlava, Hlavin,
Hlozanek, Hlavinka, Hlubik, Hluboka, Hlad,
Hladky, Hladinec, Hladik, Hladacek,
Hlas, Hladney, Hluba

Here's another list of Czech Hlast Names that I ran across at: Czech Genealogy There's some duplicates and alternative spellings.

Hlad, Hlada, Hlade, Hladek, Hladik, Hladky, Hlas, Hlava,
Hlavac, Hlavace, Hlavacek, Hlavacheck, Hlavaty, Hlavfka,
Hlavik, Hlavin, Hlavinka, Hlawa, Hlawenka, Hlebak,
Hlebik, Hlebonova, Hliboki, Hlidek, Hlina, Hlinak,
Hlinovsky, Hlivka, Hlivko, Hlouskova, Hlouslova, Hlovach,
Hlozek, Hlozik, Hlubucek, Hludzik,

Slovak

Hladick, Hladik, Hlatky, Hlavac,
Hlavcak, Hlipala, Hlozsek.

Need to know more about Slovak ancestors?

Polish

Hlusko, Hlywa, Hladyszewski,
Hladek, Hladis, Hladczuk

Ukrainian

Hladchuk, Hladkyj, Hladis, Hladuvka,
Hladun, Hladnik, Hlatky, Hlady, Hleuka

Serbian

There's got to be some, I've seen them, I was, however, remiss, in not writing them down.

Croatian

Hlaban, Hlaj

Slovenian

Hlabse, Hladyk

I was sent these by Peter Hawlina,
who can be reached at Slovenian Names
or
Slovenian Genealogy

He wrote me:
I got those names from the phone book:

Hlaca, Hlacar, Hlacer, Hlacun,
Hlad, Hlade, Hladen, Hladic,
Hladin, Hladky, Hladnic, Hladnik (most frequent),
Hladnjak, Hlaj, Hlapcic, Hlapse,
Hlastan, Hlastec, Hlatan,
Hlavac (one only:) probably a Czech who moved South
Hlavaty, Hleb, Hlebanja, Hlebce,
Hlebcar, Hlebec, Hlebic, Hlebink,
Hlebs, Hlecer, Hlede, Hlep,
Hlevnjak, Hlis, Hlisc, Hlisæ,
Hluchy, Hlupic, Hlusicka.

He added:
There are about 1000 occurances in the phone book.
Names on HL are 'related' to those on GL that are more frequent
(more that 3000 hits in the phone book).
There is an explanation of my name that tells it originates from Glava (Hlava)(Head in English) - Hlava > Hlavina > Havlina > Hawlina.

Lep pozdrav (means: to your health, keep your health)

Burmese

Hla, Hlaing, Hlaung

Zulu

Hlabangani, Hlabathi, Hlatshwayo, Hlathu, Hlongwe

Zimbabwe names

Hlatshwayo, Hlengwa, Hlongwane, Hlubi,
Hlomuka, Hlabangane.

Can you help me with these?

Hlafka, Hlal, Hlavka, Hlebka,
Hlina, Hlaca, Hliva, Hlohovsky,
Hlousek, Hluchy, Hlasnick, Hladunin,
Hladio, Hladilo

Now Hlook at this Hlist:

Some of these are already hlisted, some are spelling variants and others, well, are just news to me:

HLA ...

HLABAN, HLACHER, HLAD, HLADE, HLADEK, HLADICK, HLADICS, HLADIK,
HLADIL, HLADILEK, HLADIN, HLADIO, HLADISH, HLADKA, HLADKI, HLADKY,
HLADLEK, HLADO, HLADO POHUNEK OUMKVA, HLADSCHENKO, HLADUN, HLADY,
HLADZIO, HLAFCAK, HLAFTER, HLAS, HLATKI, HLATKY, HLATPY,
HLAVA, HLAVAC, HLAVACEK, HLAVACS, HLAVAJ, HLAVATA, HLAVATI, HLAVATIJ,
HLAVATY, HLAVCEK, HLAVCSEK, HLAVEK, HLAVIK, HLAVINKA,
HLAVKA, HLAVNA, HLAVNICKA, HLAVSA, HLAWA, HLAWATY,
HLAWENSCI, HLAWENSKY, HLAWKA, HLAWNICKA, HLAWSA

HLE...

HLEBA, HLEBAR, HLEBIK, HLEBOF, HLEBOUSKI, HLEBOWICZ, HLEDIK, HLESPIES,
HLEUKA, HLEVI

HLI...

HLIBOKI, HLINA, HLINAK, HLINEK, HLINKA, HLINKO, HLINOV, HLINOVSKY,
HLINOWSKY, HLITKY, HLIVA

HLO....

HLOBEK, HLOBEN, HLOCOMB, HLODAK, HLOOKOFF, HLOPINA, HLOPKO,
HLOPOV,
HLOSKA, HLOTS, HLOUSEK, HLOUSKOVA, HLOZEK

HLU...

HLUBUCEK, HLUBUCEK, HLUCHANOVA, HLUDZENSKI, HLUDZIK,
HLUSCHEWSKYJ, HLUSCHNIOW, HLUSKO, HLUZEK, HLUZNIOW, HLUZSNIOW

HLY...

HLYAFZ, HLYEBAK, HLYNIANSKY, HLYNOW, HLYNOWSKI, HLYWA, HLYWKA

Is this enough names? I don't think so, I'm sure there's more

I'm still trying to find the time to sort out this above Hlist, just be patient please.