What are the justifications and historical reasons regarding the choice between the words 'calculus' and 'algebra'?
What is in a name? Calculus is called analysis in some  languages
other than English, while the word calculus itself means computation.

The name π-calculus was most likely chosen by Milner because it has
to do with computation, and is intended to be for parallel computation
similar to what $\lambda$-calculus is for classical sequential computation.
Computation is actually the original meaning of calculus,
referring to pebbles used as counters in ancient time.

The word algorithm, as everyone knows, comes from the name
al-Khwarizmi (the man from Khiva, a city formerly called Khwarezm), given to the 9th century Persian
mathematician Abū Ja‘far Muhammad ibn Mūsa. Algebra comes from the
name of the treatise Hisab al-jabr wa'l muqabala, that he wrote about
the resolution of equations.

Al-Khwarizmi systematized the study of equations (algebra), and gave
procedural techniques to solve them (algorithms), which implies some form of computation (calculus). Could this be seen
as a kind of Curry-Howard situation, where the mathematics for proving
go in hand with the corresponding algorithms to actually compute ?

Names may be chosen for strange reasons, and their meaning evolves
along with the objects they initially denote. The internationalization of sciences also leads to different interpretations of words, as the same word (or its local variant) may have a different meaning in different country (and that is also true is other areas of language, possibly creating some awkward situations).

This issue has already been discussed on math.SE.



Further remarks

Actually, according to wikipedia, Analysis is used in all languages,
English included, with the same meaning. English appears to use the
word Calculus which refers only to elementary concepts of Mathematical
Analysis, differential and integral calculus. If you look for the
English Calculus in wikipedia, you find out that translation is
missing for many languages (no equivalent entry in German or French
for example), and when an entry is proposed for another language it
may corresponds to a different meaning (Cálculo in Spanish is for
calculation or computation, as it is in some other languages).

However, Cálculo in Portuguese has the same meaning as in English and
covers the same topics. They actually explain, for Portuguese, the
origin of this use of the word, and the explanation is likely to be
the same in English. Calculus is very simply an abbreviation for
"differential and integral calculus". And indeed, it corresponds to
computations expressed with algorithms, and is, in this sense, close
to Algebra.

I was mislead, in understanding the question and writing the first
part of my answer, because I took Calculus to mean the whole of
Mathematical Analysis, as there is no single word in my own language
to cover specifically differential and integral calculus. Comments
show that I am not the only non-american user to be thus mislead.

Hence there is no linguistic inconsistency. The name λ-calculus
denotes a formalisation of algorithms and computation, and the use of
the word calculus is adequate. From it was derived the name π-calculus
for parallel computations.

Note that initially, calculus just means computation (calculation has
a connotation as pertaining to numbers). When applied to a specific
domain, it is qualified so that the domain is explicit (integral
calculus, π-calculus, ...). The problem comes from the fact that it
has a common use in some languages, including English and Portuguese,
where it is domain specific without making the domain explicit, while also retaining its more general use.