HL is one of the oddest consonant clusters to start any name or word with; hlots of us hlive with it.
Hleagues

There's always someone living with the HL thing.

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, Hlavac, 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,

      
That's 59 Czech names so far, I assume there's more.

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

      That's only 8 truly Slovak names, though many if not most
of the Czech names are undoubtedly found in Slovakia.

Polish
Hlusko, Hlywa, Hladyszewski,
Hladek, Hladis, Hladczuk

      Just six found so far from north of the Tatry Mountaints.

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. But given the place names
and the basics of the hlanguage they hlurk there somewhere.

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"

      He signed it: Lep pozdrav (means: to your health, keep
your health)

Burmese
Hla, Hly, Hlaing, Hlaung

Zulu
Hlabangani, Hlabathi, Hlatshwayo, Hlathu, Hlongwe

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

      These are all the names I know for sure, so far, and with
these last three languages it is interesting to note that the
British missionaries who transliterated the languages into
Latin Letters (and it had to be British Missionaries!) they felt
compelled to use the HL combination to represent the sound
they need to portray to the HLless.
      Given the distribution of words and place names in these
hlanguages there have got to be more Hlast names!

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, 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.