The term Dharmānusārin would mean "one who follows in the Dharma" in Sanskrit. Please see the definition in this dictionary entry.
The term Śraddhānusārin would mean "one who follows in faith" in Sanskrit. Please see the definition in this dictionary entry.
The words Dharma and Śraddhā can be merged with anusārin according to sandhi rules.
On this page, from S.N. Goenka's Keynote address at the International Bauddha Mahotsav (Buddhist Conference), at Sarnath, India in 1998:
If I had been aware, much earlier, that this conference was named as
'Bauddha Mahotsav', then I would have suggested that a more
appropriate name would be 'Buddha Mahotsav', or 'Dhamma Mahotsav', or
even 'Tiratana Mahotsav'. This is because in the entire ancient
literature of the Buddha's teachings, commentaries and
sub-commentaries, amongst a total of 59,150 pages containing 9,285,755
words, the word 'Bauddha' is very conspicuously absent. The Buddha
never taught 'Buddhism' or 'Bauddh Dharma'. He never taught a
religion, nor did he convert anyone to an organized religion. He
taught Dhamma (Dharma) - the universal laws of nature - and inspired
people to follow Dhamma.
Those who followed the teachings of the Buddha were never called
'Bauddh' (Buddhist) during the time of the Buddha, and even till about
500 years later. Throughout this huge literature, we find only the
following words referring to those practicing the Buddha's teachings:
Dhammi (Dharmi), Dhammiko (Dharmika), Dhammattho (Dharmastha),
Dhammacari (Dharmacari), Dhammavihari (Dharmavihari), Dhammanusari
We don't know when, where, by whom and why the use of the word
'Bauddh' first began, and so also the use of the words 'Buddhism' and
'Buddhist'. When we say that the teachings of the Buddha are 'Bauddh
Dharama' (or Buddhism), and say his followers are Bauddh (or
Buddhists), obviously it means that the teachings are meant only for
people claiming to be 'Bauddha' or 'Buddhists'. Whereas the Buddha
declared so emphatically that Dhamma is infinite - "appamano dhammo".
When the teachings are called Buddhist, or ‘Bauddh Dharma' or
Buddhism, then most of the suffering people of the world will get
frightened thinking that they are being converted from one particular
religion to another, and be deprived of the universal teaching. But
when Buddha's teachings are given under the original, true
nomenclature of ‘Dhamma', and not any other terminology, then people
are reassured of the basic fact that the Buddha's teachings are not
just meant for any one religion. So people from any background will
have no hesitation accepting his teachings.
Our research at Igatpuri has shown us that till about 500 years after
Buddha, the word ‘Bauddh' was not found in any ancient spiritual
literature of India-the literature in the Buddha tradition, Mahavir
tradition, or Vedic tradition. The distinguished scholars assembled
here may help us make a proper research as to when usage of this word
It is most important to remember that the Buddha's teachings are not
meant to be limited to any particular sect. His teachings are
universal. And if we see the Enlightened One's teachings in proper
perspective, it is clear that the original teachings of the Buddha are
totally universal and non-sectarian.