Is there a word for "not pronouncing any r's"?

Some find it difficult to form an "r" sound, and some are able to, but just don't. I'm looking for a word which means "not pronouncing r's", without implying inability to pronounce them, though that may be the case.

Specifically, I'd like a word which mean "not pronouncing any r's", but if there's a word which means "not pronouncing some r's" (as in many dialects), that would be interesting to know too.

The Wikipedia article on rhotacism gives one definition of that word as “the inability to or difficulty in pronouncing r”.

Non-rhotic may be what you're looking for:

English pronunciation can be divided into two main accent groups: a rhotic (pronounced /ˈroʊtɨk/, sometimes /ˈrɒtɨk/) speaker pronounces a rhotic consonant in words like hard; a non-rhotic speaker does not. That is, rhotic speakers pronounce /r/ in all positions, while non-rhotic speakers pronounce /r/ only if it is followed by a vowel sound in the same phrase or prosodic unit (see "linking and intrusive R").

In linguistic terms, non-rhotic accents are said to exclude the sound [r] from the syllable coda before a consonant or prosodic break. This is commonly (if misleadingly) referred to as "post-vocalic R".

^Wikipedia